Unbounded Operator Algebras and Representation Theory - Operator Theory: Advances and Applications, 37

Schmüdgen, K.

ISBN 10: 3764323213 / ISBN 13: 9783764323219

Published by Birkhäuser, Boston, 1990

About this Item

Very minor shelf wear ONLY. ; Algebras of unbounded operators in Hilbert space naturally arise in unitary representation theory of Lie groups and quantum field theory. They appear as representations of Lie algebras or as field operator systems. While some foundational tools, such as the weak commutant, were introduced earlier, a systematic study began in the 1970s, led by Borchers, Lassner, Powers, Uhlmann, and Vasiliev. The theory connects with areas like von Neumann algebras, locally convex spaces, distribution theory, and noncommutative probability. ; 17.7 x 23.6 x 2.9 cm; 380 pages.

Seller Inventory # LCB62262

Bibliographic Details

• Title: Unbounded Operator Algebras and Representation Theory - Operator Theory: Advances and Applications, 37
• Publisher: Birkhäuser, Boston
• Publication Date: 1990
• Language: English
• ISBN 10: 3764323213
• ISBN 13: 9783764323219
• Binding: Hardcover
• Edition: First Edition; First Impression.
• Condition: Near Fine
• Dust Jacket Condition: No Dust Jacket

About this title

Synopsis

*-algebras of unbounded operators in Hilbert space, or more generally algebraic systems of unbounded operators, occur in a natural way in unitary representation theory of Lie groups and in the Wightman formulation of quantum field theory. In representation theory they appear as the images of the associated representations of the Lie algebras or of the enveloping algebras on the Garding domain and in quantum field theory they occur as the vector space of field operators or the *-algebra generated by them. Some of the basic tools for the general theory were first introduced and used in these fields. For instance, the notion of the weak (bounded) commutant which plays a fundamental role in thegeneraltheory had already appeared in quantum field theory early in the six­ ties. Nevertheless, a systematic study of unbounded operator algebras began only at the beginning of the seventies. It was initiated by (in alphabetic order) BORCHERS, LASSNER, POWERS, UHLMANN and VASILIEV. J1'rom the very beginning, and still today, represen­ tation theory of Lie groups and Lie algebras and quantum field theory have been primary sources of motivation and also of examples. However, the general theory of unbounded operator algebras has also had points of contact with several other disciplines. In particu­ lar, the theory of locally convex spaces, the theory of von Neumann algebras, distri­ bution theory, single operator theory, the momcnt problem and its non-commutative generalizations and noncommutative probability theory, all have interacted with our subject.