Displaying similar documents to “Direct sums of irreducible operators”

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

Santtu Ruotsalainen (2012)

Studia Mathematica

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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...

Concerning the sum of two continua each irreducible between the same pair of points

John Kline (1925)

Fundamenta Mathematicae

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The first part of the paper answers the question whether two different continua, each irreducible between the same pair of points could have a sum irreducible between two of its points. The second part shows certain properties of continua irreducible between the same pair of points and having the above mentioned property with respect to their sum.

On a method of determining supports of Thoma's characters of discrete groups

Ernest Płonka (1997)

Annales Polonici Mathematici

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We present a new approach to determining supports of extreme, normed by 1, positive definite class functions of discrete groups, i.e. characters in the sense of E. Thoma [8]. Any character of a group produces a unitary representation and thus a von Neumann algebra of linear operators with finite normal trace. We use a theorem of H. Umegaki [9] on the uniqueness of conditional expectation in finite von Neumann algebras. Some applications and examples are given.

A comment on free group factors

Narutaka Ozawa (2010)

Banach Center Publications

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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.