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

Santtu Ruotsalainen (2012)

Studia Mathematica

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 is constructed....

On an inclusion between operator ideals

Manuel A. Fugarolas (2011)

Czechoslovak Mathematical Journal

Let 1 ≤ q < p < ∞ and 1 / r : = 1 / p max ( q / 2 , 1 ) . We prove that ℒ r , p ( c ) , the ideal of operators of Geľfand type l r , p , is contained in the ideal Π p , q of ( p , q ) -absolutely summing operators. For q > 2 this generalizes a result of G. Bennett given for operators on a Hilbert space.

On an integral-type operator from Privalov spaces to Bloch-type spaces

Xiangling Zhu (2011)

Annales Polonici Mathematici

Let H(B) denote the space of all holomorphic functions on the unit ball B of ℂⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. We study the integral-type operator C φ g f ( z ) = ∫ 0 1 ℜ f ( φ ( t z ) ) g ( t z ) d t / t , f ∈ H(B). The boundedness and compactness of C φ g from Privalov spaces to Bloch-type spaces and little Bloch-type spaces are studied

On asymptotic cyclicity of doubly stochastic operators

Wojciech Bartoszek (1999)

Annales Polonici Mathematici

It is proved that a doubly stochastic operator P is weakly asymptotically cyclic if it almost overlaps supports. If moreover P is Frobenius-Perron or Harris then it is strongly asymptotically cyclic.

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