Search results for "Operator Algebra"

MR2544061 Ludkovsky, S. V. Algebras of operators in Banach spaces over the quaternion skew field and the octonion algebra. J. Math. Sci. (N. Y.) 144 …

2010

Locally Convex Quasi *-Algebras and their Representations

2020

This book is a review of the work the authors have done in the past 20 years on the theory of locally convex quasi *-algebras

Applications of topological *-algebras of unbounded operators to modified quons

2002

In this paper we discuss some applications of topological *-algebras of unbounded operators to what we call Modified Quons (MQ). In particular, the existence of the thermodynamical limit for some models of free and interacting modified quons is proved in the same framework proposed by the author in a recent paper for ordinary bosons.

States and representations of CQ∗ -algebras

1994

A class of quasi *-algebras which exhibits some analogy with C*-algebras is studied. The extension of some properties of C*-algebras which are relevant for physical applications (such as the GNS-representation) is discussed. Quasi *-algebras of linear operators in rigged Hilbert space are shown to be typical examples of the developed framework.

Norm continuity and related notions for semigroups on Banach spaces

1996

We find some conditions on a c0-semigroup on a Banach space and its resolvent connected with the norm continuity of the semigroup. We use them to get characterizations of norm continuous, eventually norm continuous and eventually compact semigroups on Hilbert spaces in terms of the growth of the resolvent of their generator.

Modular Structures on Trace Class Operators and Applications to Landau Levels

2009

The energy levels, generally known as the Landau levels, which characterize the motion of an electron in a constant magnetic field, are those of the one-dimensional harmonic oscillator, with each level being infinitely degenerate. We show in this paper how the associated von Neumann algebra of observables displays a modular structure in the sense of the Tomita–Takesaki theory, with the algebra and its commutant referring to the two orientations of the magnetic field. A Kubo–Martin–Schwinger state can be built which, in fact, is the Gibbs state for an ensemble of harmonic oscillators. Mathematically, the modular structure is shown to arise as the natural modular structure associated with the…

Malliavin calculus of Bismut type without probability

2007

We translate in semigroup theory Bismut's way of the Malliavin calculus.

Locally convex quasi $C^*$-normed algebras

2012

Abstract If A 0 [ ‖ ⋅ ‖ 0 ] is a C ∗ -normed algebra and τ a locally convex topology on A 0 making its multiplication separately continuous, then A 0 ˜ [ τ ] (completion of A 0 [ τ ] ) is a locally convex quasi ∗-algebra over A 0 , but it is not necessarily a locally convex quasi ∗-algebra over the C ∗ -algebra A 0 ˜ [ ‖ ⋅ ‖ 0 ] (completion of A 0 [ ‖ ⋅ ‖ 0 ] ). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C ∗ -normed algebra, aiming at the investigation of A 0 ˜ [ τ ] ; in particular, we study its structure, ∗-representation theory and functional calculus.

Applications of Topological *-Algebras of Unbounded Operators

1998

In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the time evolution of two interacting models of matter and bosons. We show that for all these systems it is possible to build up a common framework where the thermodynamical limit of the algebraic dynamics can be conveniently studied and obtained.

Clarkson-McCarthy inequalities with unitary and isometry orbits

2020

Abstract A refinement of a trace inequality of McCarthy establishing the uniform convexity of the Schatten p-classes for p > 2 is proved: if A , B are two n-by-n matrices, then there exists some pair of n-by-n unitary matrices U , V such that U | A + B 2 | p U ⁎ + V | A − B 2 | p V ⁎ ≤ | A | p + | B | p 2 . A similar statement holds for compact Hilbert space operators. Another improvement of McCarthy's inequality is given via the new operator parallelogramm law, | A + B | 2 ⊕ | A − B | 2 = U 0 ( | A | 2 + | B | 2 ) U 0 ⁎ + V 0 ( | A | 2 + | B | 2 ) V 0 ⁎ for some pair of 2n-by-n isometry matrices U 0 , V 0 .