[permalink] [id link]
Though algebras of operators are studied in various contexts ( for example, algebras of pseudo-differential operators acting on spaces of distributions ), the term operator algebra is usually used in reference to algebras of bounded operators on a Banach space or, even more specially in reference to algebras of operators on a separable Hilbert space, endowed with the operator norm topology.
from
Wikipedia
Some Related Sentences
Though and algebras
Though there is a theory for von Neumann algebras on non-separable Hilbert spaces ( and indeed much of the general theory still holds in that case ) the theory is considerably simpler for algebras on separable spaces and most applications to other areas of mathematics or physics only use separable Hilbert spaces.
Though and operators
Though large wide-web flexo rolls are only maneuverable by overhead crane, on smaller presses anilox rolls are often handled directly by operators.
Though coined earlier, the term photonics came into common use in the 1980s as fiber-optic data transmission was adopted by telecommunications network operators.
Though most commercial traffic has now ceased operation using Morse it is still popular with amateur radio operators.
Though rare, more experienced botnet operators program command protocols from scratch.
Though it was introduced as a tool to promote competition in the heavily monopolized wireline telecommunications industry, number portability became popular with the advent of mobile telephones, since in most countries different mobile operators are provided with different area codes and, without portability, changing one's operator would require changing one's number.
Though the operators initially refused, they later accepted the city's offer of $ 100, 000 ($ 2, 095, 000, adjusted for inflation ) in 1915.
Though most agencies provide a broader range of service offering, at the extremes are the two extremes are the traditional providers and the niche operators.
Though Ponzi schemes have existed since at least the early 1900s, the rise of digital payment systems has made it much easier for operators of such websites to accept payments from people worldwide .< ref >
Though considered to be a " mechanic's oversight ," the FAA nevertheless wired all 707 operators to inform them of the potential danger of the assembly.
Though intended to be exclusive to women, most train operators in Japan allow male elementary school pupils, disabled persons, and their assistants to board women-only cars.
Though it is frequently described as a prostitutes ' rights group, COYOTE's mission includes advocating for all varieties of sex workers of all genders, including strippers, phone sex operators and adult film performers.
Though and are
Institutionalization Though undoubtedly all six processes are operative within the whole social system and its subsystems, two processes that are of crucial importance to this study will be singled out for particular emphasis.
Though they are often heard clairaudiently, as if a voice were speaking them, in other cases they are apprehended visually as symbols: a slope to signify the name `` Hill '', for instance.
Though there are many exceptions, which we have noted in preceding pages, white wine is as a rule best consumed between two and six years old, and red wines, nowadays, between three and ten.
Though the sales gains these two dealers are experiencing are above average for their business, farm equipment sales are climbing in most rural areas.
Though no longer able to turn out his protoplasmic pen-and-ink sketches ( several old favorites are scattered through the present volume ) Thurber has retained unimpaired his vision of humor as a thing of simple, unaffected humanness.
Though Aristotle wrote many elegant treatises and dialogues ( Cicero described his literary style as " a river of gold "), it is thought that the majority of his writings are now lost and only about one-third of the original works have survived.
Though the prokaryotic cyanobacteria ( commonly referred to as blue-green algae ) were traditionally included as " algae " in older textbooks, many modern sources regard this as outdated as they are now considered to be bacteria.
Though the prison chaplain accuses the state of stripping Alex of free will, the government officials on the scene are pleased with the results and Alex is released into society.
Though anarcho-capitalists are known for asserting a right to private ( individualized or joint non-public ) property, some propose that non-state public or community property can also exist in an anarcho-capitalist society.
Though the are has fallen out of use, the hectare is still commonly used to measure land:
Though most of the early Waldorf schools were teacher-founded, the schools today are usually initiated and later supported by an active parent community.
Though rarely used by modern conventional military units, abatises are still officially maintained in United States Army and Marine Corps training.
Though they admit that plants must be destroyed for the sake of food, they accept such violence only inasmuch as it is indispensable for human survival, and there are special instructions for preventing unnecessary violence against plants.
Though, theoretically, all life forms are said to deserve full protection from all kinds of injury, Jains admit that this ideal cannot be completely implemented in practice.
Though authors are not allowed to charge for access to copies of their work, downloading a copy from the ACM site requires a paid subscription.
Though most of the ministries are seated in Berlin, some of them, as well as some minor departments, are seated in Bonn, the former capital of West Germany.
Though most of these laws have been relaxed or repealed in most states, they are still strictly enforced in some other states.
Though intentional walks are recorded as such in the records of the official scorer, they are combined with standard, non-intentional walks when calculating a player's on-base percentage, and have only received a separate column in a player's statistics since 1955.
Though much more expensive than steel, there are now aluminium alloys available that will not corrode in salt water, and an aluminium boat built to similar load carrying standards could be built lighter than steel.
Though and studied
Though Rudolf Steiner studied natural science at the Vienna Technical University at the undergraduate level, his doctorate was in epistemology and very little of his work is directly concerned with the empirical sciences.
Though Gregory conveys political and other messages through the Historia, and these are studied very closely, historians generally agree that this contrast is the central and ever-present narrative device.
Though Dōgen assiduously studied the kōans, he became disenchanted with the heavy emphasis laid upon them, and wondered why the sutras were not studied more.
Though he was initially unsure if he wanted to go to university, Fox's mother convinced him to enrol at Simon Fraser University, where he studied kinesiology as a stepping stone to becoming a physical education teacher.
Though presently theoretical, another near-realization of Maxwell's demon is a water filter studied by David Cohen-Tanugi and Jeffrey C. Grossman of MIT.
Though a local educated worker at the Jiangyong Cultural Office ( Zhou Shuoyi ) had collected, studied and translated many Nüshu texts into standard Chinese, he was unable to draw outside attention to the script until a report was submitted to the central government on this subject in 1983.
Though genetic defects causing iron deficiency have been studied in rodents, there are no known genetic disorders of human iron metabolism that directly cause iron deficiency.
Though he studied at the University of California, Berkeley, he was still virtually self-taught when he began writing music of his own, but in the early 1920s he had lessons from Arthur Bliss ( then in Santa Barbara ) and the senior American composer and researcher of American Indian ( then called " Red Indian ") music, Arthur Farwell.
Though interested in being a soldier, he studied divinity, and was licensed by the presbytery of Edinburgh in 1745.
Though Bible codes have been postulated and studied for centuries, the subject has been popularized in modern times by Michael Drosnin's book The Bible Code.
Though not studied quantitatively, the physical properties of liquid elemental mercury limit its absorption through intact skin and in light of its very low absorption rate from the gastrointestinal tract, skin absorption would not be high.
Though one might think that these " circadian rhythms " are controlled simply by the presence or absence of light, nearly every animal that has been studied has been shown to have a " biological clock " that yields cycles of activity even when the animal is in constant illumination or darkness.
Though he is said to have studied at the University of Cambridge his name is not found in any university or college records.
Though links are being studied with the state of Goiás, and other interior locations, in terms of product flow for export.
Though he had never studied visual arts in the academic sense, Carigiet's early graphic design was already strongly influenced by contemporary artists, such as El Lissitzky, whose use of photomontage in a poster announcing the exhibition of Russian avant-garde artists in Zurich, in 1928, inspired the design of a political campaign poster for Zurich's mayor Emil Klöti.
Though this came as somewhat of a shock to the American public, those who knew him privately were not surprised, as Gage had previously studied spiritualism, astrology, and prophesized the death of his own brother through a " psychic flash ".< ref >
Though there is no contemporary evidence, it has been claimed that he studied with Costanzo Porta ( Mompellio 2001 ), becoming choirmaster at the cathedral in Mantua by 1594.
Though Lawrence studied law, he entered the United States Navy as a midshipman in 1798.
Though Gabirol as a philosopher was not studied by the Jewish community, Gabirol as a poet kept alive the remembrance of the ideas of the philosopher ; for his best-known poem, Keter Malkut (" Royal Crown "), is a philosophical treatise in poetical form, the " double " of the Fons Vitæ.
Though he had not studied theology, he was ordinated as a priest in Treptow's St. Mary's Church in 1509, and served as a vicar at the Kanonikerkolleg of that church thereafter.
Though the education she received there was excellent, Helena often also studied on her own.
Though he originally studied law, he quickly realized his principal love was music, and he acquired a doctorate at Munich University, focusing on instrumental music of the late Renaissance and early Baroque eras, in particular music for the viola da gamba.
Though born in Nebraska, Ruscha lived some 15 years in Oklahoma City before moving to Los Angeles in 1956 where he studied at the Chouinard Art Institute ( now known as the California Institute of the Arts ) under Robert Irwin and Emerson Woelffer from 1956 through 1960.
1.522 seconds.