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 )

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 ") )

*- i ( Afghanistan → Afghanistani, Azawad → Azawadi, Azerbaijan → Azerbaijani, Bahrain → Bahraini, Bangladesh → Bangladeshi, Bengal → Bengali, Bihar → Bihari, Dagestan → Dagestani, Desh → Desi, Gujarat → Gujarati, Hyderabad → Hyderabadi, Iraq → Iraqi, Israel → Israeli ( in the Modern State of Israel ), Kashmir → Kashmiri, Kazakhstan → Kazakhstani ( also " Kazakh "), Kuwait → Kuwaiti, Nepal → Nepali, Oman → Omani, Pakistan → Pakistani, Punjab → Punjabi, Qatar → Qatari, Rajasthan → Rajasthani, Sindh → Sindhi, Somalia → Somali ( not Somalian ), Tajikistan → Tajikistani ( also " Tajik "), United Arab Emirates → United Arab Emirati, Uzbekistan → Uzbekistani ( also " Uzbek "), Yemen → Yemeni, Yerevan → Yerevani ), mostly for Middle Eastern and South Asian locales and in Latinate names for the various people that ancient Romans encountered ( e. g. Allemanni, Helvetii )

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 ).

*- ijo /- ija ( lagarto, " lizard " → lagartija " wall lizard "),

The etymology of Agmundr is Old West Scandinavian agi-(" awe, terror ") or possibly the German * ag-(" point, weapon point "), with-mundr, from Old West Scandinavian *- munduR (" protection ").

Old Irish ibar " yew-tree ",,, " alder buckthorn ", " alder buckthorn "), combined with the suffix *- āko ( n ) " place " ( cf.

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.

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.

However, this Proto-Algonquian term most likely was ultimately derived from a form *- a · towe ·, meaning simply " to speak a foreign language ", which would make it similar to the etymology of the Greek " Barbarian ".

In Attic Greek an original genitive singular ending *- osyo after losing the s ( as happens in all the dialects ) lengthens the stem o to the spurious diphthong-ou ( see above under Phonology, Vowels ): logos " the word ", logou from * logosyo, " of the word ".

" 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 *

*- blogpost " William Joynson-Hicks ", 3 February 2010,

*- ( 1961 ) " John James Waterston and the kinetic theory of gases ", American Scientist, vol.

*- stan, a Persian suffix meaning " home of ", " place of "

*- ian, similar to above case but with the addition of the plural suffix "- an ", common among Persians and Armenians.

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

* both Etruscan and Lemnian share two unique dative cases, type-I *- si and type-II *- ale, shown both on the Lemnos Stele ( Hulaie-ši " for Hulaie ", Φukiasi-ale " for the Phocaean ") and in inscriptions written in Etruscan ( aule-si " To Aule " on the Cippus Perusinus as well as the inscription mi mulu Laris-ale Velχaina-si " I was blessed for Laris Velchaina ").

* C *- algebra: A Banach algebra that is a closed *- subalgebra of the algebra of bounded operators on some Hilbert space.

By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.

A C *- algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties:

The algebra M < sub > n </ sub >( C ) of n-by-n matrices over C becomes a C *- algebra if we consider matrices as operators on the Euclidean space, C < sup > n </ sup >, and use the operator norm ||.|| on matrices.

which extends verbatim to positive functionals on C *- algebras.

Here C < sub > b </ sub >( X ) denotes the C *- algebra of all continuous bounded functions on X with sup-norm.

However, instead of simply considering the space of ultrafilters on, the right way to generalize this construction is to consider the Stone space of the measure algebra of: the spaces and are isomorphic as C *- algebras as long as satisfies a reasonable finiteness condition ( that any set of positive measure contains a subset of finite positive measure ).

*- Across the seas of darkness / The good green Earth is bright – / Oh, Star that was my homeland / Shine down on me tonight .-

* Von Neumann algebra: a *- algebra of operators on a Hilbert space equipped with the weak operator topology.

*- More on MSX disease

*- informations on recordings with modern use of the old instruments

The concept of normal matrices can be extended to normal operators on infinite dimensional Hilbert spaces and to normal elements in C *- algebras.

*- For details on Stukeley and Isaac Newton

* Multiplier algebra, a construction on C *- Algebras and similar structures.

A *- algebra A is a *- ring that is an associative algebra over a commutative *- ring R, with the * agreeing on.

A *- operation on a *- ring is an operation on a ring that behaves similarly to complex conjugation on the complex numbers.