Displaying similar documents to “Commuting operators and class functions.”

On a Weyl-von Neumann type theorem for antilinear self-adjoint operators

Santtu Ruotsalainen (2012)

Studia Mathematica

Similarity:

Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl-von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear self-adjoint operator is the sum of a diagonalizable operator and of a compact operator with arbitrarily small Schatten p-norm. On the way, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators...

A comment on free group factors

Narutaka Ozawa (2010)

Banach Center Publications

Similarity:

Let M be a finite von Neumann algebra acting on the standard Hilbert space L²(M). We look at the space of those bounded operators on L²(M) that are compact as operators from M into L²(M). The case where M is the free group factor is particularly interesting.

Factorization of operators on C*-algebras

Narcisse Randrianantoanina (1998)

Studia Mathematica

Similarity:

Let A be a C*-algebra. We prove that every absolutely summing operator from A into ℓ 2 factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite-dimensional examples that show that one cannot replace the 4-Schatten-von Neumann class by the p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of capacity ε → N(ε) so that if A is a C*-algebra and T ∈ Π 1 ( A , ℓ 2 ) with π 1 ( T ) ≤ 1 , then for every ε >0, the...

Exponentials of normal operators and commutativity of operators: a new approach

Mohammed Hichem Mortad (2011)

Colloquium Mathematicae

Similarity:

We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.

Fuglede-type decompositions of representations

Marek Kosiek (2002)

Studia Mathematica

Similarity:

It is shown that reducing bands of measures yield decompositions not only of an operator representation itself, but also of its commutant. This has many consequences for commuting Hilbert space representations and for commuting operators on Hilbert spaces. Among other things, it enables one to construct a Lebesgue-type decomposition of several commuting contractions without assuming any von Neumann-type inequality.

Subadditive measures on projectors of a von Neumann algebra

Leszek J. Ciach

Similarity:

CONTENTSIntroduction...............................................................................................................................................5§0. Fundamental definitions and notations...............................................................................................7§1. Subadditive measure on projectors of a von Neumann algebra.........................................................8§2. m-measurable operators. Convergence in measure.........................................................................10§3....