Moreover ( and more embarrassingly, although this is essentially trivial ), mathematicians usually write the dual entity not at the first place, as the physicists do, but at the second one, and they don't use the *- symbol, but an overline ( which the physicists reserve to averages ) to denote conjugate-complex numbers, i. e. for scalar products mathematicians usually write

In the case of C *- algebras, any *- homomorphism π between C *- algebras is non-expansive, i. e. bounded with norm ≤ 1.

Among the typological features of Egyptian that are typically Afroasiatic are: fusional morphology, consonantal lexical roots, a series of emphatic consonants, a three-vowel system / a i u /, nominal feminine suffix *- at, nominal m -, adjectival *- ī, and characteristic personal verbal affixes.

A *- homomorphism is algebra homomorphism that is compatible with the involutions of A and B, i. e.,

Given a state ρ of A, there is a *- representation π of A with distinguished cyclic vector ξ such that its associated state is ρ, i. e.

It follows that the *- algebra generated by u < sub > ij </ sub > for all i, j and κ ( u < sub > ij </ sub > ) for all i, j is a Hopf *- algebra: the counit is determined by for all i, j ( where is the Kronecker delta ), the antipode is κ, and the unit is given by

:* There exists a C *- algebra homomorphism Δ: C → C ⊗ C ( where C ⊗ C is the C *- algebra tensor product-the completion of the algebraic tensor product of C and C ) such that for all i, j ( Δ is called the comultiplication );

A representation of the compact matrix quantum group is given by a corepresentation of the Hopf *- algebra ( a corepresentation of a counital coassociative coalgebra A is a square matrix with entries in A ( so ) such that for all i, j and for all i, j ).

In the C *- algebraic formulation of quantum mechanics, states in this previous sense correspond to physical states, i. e. mappings from physical observables to their expected measurement outcome.

extends to a C *- isomorphism from the group C *- algebra C *( G ) of G and C < sub > 0 </ sub >( G < sup >^</ sup >), i. e. the spectrum of C *( G ) is precisely G < sup >^</ sup >.

*- i, the most common suffix used for Persian surnames.

assumed to be a commutative C *- algebra, i. e. the space of continuous functions C ( X ) on some set X.

The most probable seems the assumption that PIE */ s / was changed to */ š / after */ r /, */ u /, */ k /, */ i / completely regularly in Baltic, just like in Slavic, but the traces of the effect of RUKI law were erased by subsequent changes, such as the change of word-final *- š to *- s.

A Banach *- algebra A is a Banach algebra over the field of complex numbers, together with a map *: A → A called involution which has the following properties:

A C *- algebra, A, is a Banach algebra over the field of complex numbers, together with a map *: A → A.

A bounded linear map, π: A → B, between C *- algebras A and B is called a *- homomorphism if

*- ian ( countries: Bahamas → Bahamian, Belarus → Belarusian, Belgium → Belgian, Bermuda → Bermudian, Brazil → Brazilian, Cameroon → Cameroonian, Canada → Canadian, Chad → Chadian, Egypt → Egyptian, Ecuador → Ecuadorian, Ghana → Ghanaian, Grenada → Grenadian, Iran → Iranian ( also " Irani " or " Persian "), Jordan → Jordanian, Laos → Laotian, Louisiana → Louisianian, Maldives → Maldivian, Palestine → Palestinian, Saint Vincent → Vincentian, Trinidad → Trinidadian, Ukraine → Ukrainian ; cities / states: Adelaide → Adelaidian, Athens → Athenian, Ballarat → Ballaratian, Boston → Bostonian, Brisbane → Brisbanian ( also " Brisbanite "), Calgary → Calgarian, Canary Islands → Canarian, Cardiff → Cardiffian, Castile → Castilian, Coventry → Coventrian, Edmonton → Edmontonian, Florida → Floridian, Fort Worth → Fort Worthian, Gibraltar → Gibraltarian, Hesse → Hessian, Houston → Houstonian, Isles of Scilly → Scillonian, Lethbridge → Lethbridgian, Liverpool → Liverpudlian, Louisville → Louisvillian, Madrid → Madrilenian, Manchester → Mancunian, McKinney → McKinnian, Melbourne → Melburnian, New Guinea → New Guinian, New Orleans → New Orleanian, Oregon → Oregonian, Paris → Parisian, Peterborough → Peterborian, Phoenix → Phoenician, Saskatoon → Saskatonian ( Saskabusher ), Thrace → Thracian, Washington → Washingtonian, Wellington → Wellingtonian )

*- zadeh ,-zada ,-zoda, zad, zod, " decedent of ", common among Iranians, Azerbaijani, Tajikistani, Afghanistani, Uzbekistani and Pakistani.

*- ul-Mulk ( or ul-Molk ):-of the kingdom ; e. g. Malik Usman Khan, who served the Sultan of Gujarat as Governor of Lahore, received the title of Zubdat ul-Mulk ' best of the kingdom ' as a hereditary distinction, which was retained as part of the style of his heirs, the ruling Diwans ( only since 1910 promoted to Nawab ) of Palanpur.

Around 1943, the work of Israel Gelfand and Mark Naimark yielded an abstract characterisation of C *- algebras making no reference to operators on a Hilbert space.

*- ite ( Ann Arbor → Ann Arborite, Austin → Austinite, Brisbane → Brisbanite ( also " Brisbanian "), Chennai → Chennaite, Dallas → Dallasite, Delhi → Delhite, Denver → Denverite, Dunedin → Dunedinite, Irmo → Irmite, Israel → Israelite ( also " Israeli ", depending on the usage ; see below ), Karachi → Karachiite, Moscow → Muscovite ( also Latin " Muscovia "), New Hampshire → New Hampshirite, Perth → Perthite, Ruskin → Ruskinite, Seattle → Seattleite, Seoul → Seoulite, Springfield → Springfieldianite, Spokane → Spokanite, Tokyo → Tokyoite, Vancouver → Vancouverite, Wisconsin → Wisconsinite, Wyoming → Wyomingite ), Wenham → Wenhamite mostly for cities.

This result was proven by Israel Gelfand and Mark Naimark in 1943 and was a significant point in the development of the theory of C *- algebras since it established the possibility of considering a C *- algebra as an abstract algebraic entity without reference to particular realizations as an algebra of operators.

Proto-Celtic is reconstructed as having * werbā-' blister ' in its lexicon and the name may be a suffixed form of this lexeme meaning “ blistered one .” On the other hand, the root of the name may represent a Celtic reflex of the Proto-Indo-European root * wer-bhe-‘ bend, turn ,’ cognate with Modern English warp, followed by the durative suffix *- j-and the feminine suffix *- ā-and so might have meant “ she who is constantly bending and turning .” Another possibility is that the name is a compound of Romano-British reflexes of the Proto-Celtic elements ** Uφer-bej-ā-( upper-strike-F ) “ the upper striker .”

*- Museum of Modern Art's Collection

*- Buddhism in a Muslim State: Theravada Practices and Religious Life in Kelantan Inebnetwork-Buddhism in a Muslim State: Theravada Practices and Religious Life in Kelantan

*- Official New York State Arm Wrestling Association Featuring the NYC Big Apple Grapple International, NY Golden Arm Series and Empire State Golden Arm Tournament of Champions

As it is now known that all B *- algebras are C *- algebras ( and vice versa ), the term B *- algebra is no longer widely used.

" Jeffrey Michael Featherstone ( Introduction, Text and Translation ), Theodore Metochites ’ s poems ‘ to Himself ’ vindobonensia, XXIII, Wien: Verlag der Österreichischen Akademie der Wissenschaften, 2000 ", Scriptorium 56 ( 2002 ), p. 328 *- 330 *

*- ism ( suffix ), a suffix appended to many philosophical concepts

*- ish ( Åland → Ålandish, Britain → British, Cornwall → Cornish, Denmark → Danish, England → English, Finland → Finnish, Ireland → Irish, Kurdistan → Kurdish, Poland → Polish, Scotland → Scottish, Spain → Spanish, Sweden → Swedish, Turkey → Turkish ), mostly for countries

*- ic ( Hispania → Hispanic, Turk → Turkic ) derives from a Latinate suffix widely used outside ethnonyms ( e. g., chemical compounds ), which with regard to people is mostly used adjectivally ( Semite vs. Semitic, Arab / Arabian vs. Arabic ) to refer to a wider ethnic or linguistic group ( Turkic vs. Turkish, Finnic vs. Finnish ).

*- iot ( e ) ( Corfu → Corfiot, Cyprus → Cypriot, Phanar → Phanariote ), especially for Greek locations.

This is not a *- ring structure ( unless the characteristic is 2, in which case it's identical to the original *), as ( so * is not a ring homomorphism ), neither is it antimultiplicative, but it satisfies the other axioms ( linear, involution ) and hence is quite similar.

This suggests that one might define a noncommutative Riemannian manifold as a spectral triple ( A, H, D ), consisting of a representation of a C *- algebra A on a Hilbert space H, together with an unbounded operator D on H, with compact resolvent, such that is bounded for all a in some dense subalgebra of A.

49. 70 % of residents only have level one or two qualifications ( at least 1 GCSE pass ( A *- G ) or equivalent ), and 18. 25 % have at least level three qualiffications ( at least 2 A-levels ( A-E ) or 4 AS levels ( A-E ) or equivalent ).

As a generalization, a compact matrix quantum group is defined as a pair ( C, u ), where C is a C *- algebra and is a matrix with entries in C such that

The set of states of a C *- algebra A, sometimes denoted by S ( A ), is always a convex set.

Specifically, it shows that if M is a unital, self-adjoint operator algebra in the C *- algebra B ( H ), for some Hilbert space H, then the weak closure, strong closure and bicommutant of M are equal.

Let be a weak *- closed operator algebra contained in B ( H ), the set of all bounded operators on a Hilbert space H and for T any operator in B ( H ), let

C *- algebras are now an important tool in the theory of unitary representations of locally compact groups, and are also used in algebraic formulations of quantum mechanics.

*- ene ( Cairo → Cairene, Damascus → Damascene, Nazareth → Nazarene, Slovenia → Slovene ( also " Slovenian ") )

Given a *- ring, there is also the map.

The universal construction is also used to define universal C *- algebras of isometries.

On the other hand, a finite-dimensional representation of G can be used to generate a *- subalgebra of C ( G ) which is also a Hopf *- algebra.

*- er /- ers /- ster ( agentive, intensive, hypocoristic, also elided rhotic-a ): bonkers ( 1948 ), preggers ( 1940 ), starkers ( 1905 ), Becker, Lizzers, Hankster, Patster

*- ino ,-ina, the most used one along with-etto: paese → paesino ( village → little village ); also in baby talk and after other suffixes: bello → bellino ( pretty ), giovane → giovanotto → giovanottino ( but there are no limits to suffixation, which could continue );

*- uccio ,-uccia, hypocoristic or pejorative ( also in southern forms-uzzo ,-uzza ).

*- ise, a suffix also spelled "- ize ".

The riist " manifesto " also adopts the masculine suffix *- iĉo and the occasional epicene use of ge-to avoid any resulting confusion.

Say A is an *- algebra representation of the Lie superalgebra ( together with the additional requirement that * respects the grading and L < sup >*</ sup >=-(- 1 )< sup > La </ sup > L < sup >*</ sup >) and H is the unitary rep and also, H is a unitary representation of A.

It also guarantees a minimum fill ( except for the root node ), however best performance has been experienced with a minimum fill of 30 %– 40 % of the maximum number of entries ( B-trees guarantee 50 % page fill, and B *- trees even 66 %).

The decreased overlap of rectangles in the R *- tree is one of the key benefits over the traditional R-Tree ( this is also a consequence of the other heuristics used, not only the subtree choosing ).

There are other splitting strategies such as Greene's Split, the R *- tree splitting heuristic ( which again tries to minimize overlap, but also prefers quadratic pages ) or the linear split algorithm proposed by Ang and Tan ( which however can produce very unregular rectangles, which are less performant for many real world range and window queries ).

In addition to having a more advanced splitting heuristic, the R *- tree also tries to avoid splitting a node by reinserting some of the node members, which is similar to the way a B-tree balances overflowing nodes.

Finally, the X-tree can be seen as a R *- tree variant that can also decide to not split a node, but construct a so-called super-node containing all the extra entries, when it doesn't find a good split ( in particular for high-dimensional data ).