On a class of absolutely p-summing operators
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Tin Wong (1971)
Studia Mathematica
O. Reynov (1981)
Studia Mathematica
Nicolae Tita (1981)
Collectanea Mathematica
Michels, C. (2010)
Annals of Functional Analysis (AFA) [electronic only]
Driss Drissi (1998)
Studia Mathematica
Using [1], which is a local generalization of Gelfand's result for powerbounded operators, we first give a quantitative local extension of Lumer-Philips' result that states conditions under which a quasi-nilpotent dissipative operator vanishes. Secondly, we also improve Lumer-Phillips' theorem on strongly continuous semigroups of contraction operators.
Vasile Lauric (2021)
Czechoslovak Mathematical Journal
We prove that for normal operators the generalized commutator approaches zero when tends to zero in the norm of the Schatten-von Neumann class with and varies in a bounded set of such a class.
Driss Drissi (1997)
Studia Mathematica
In 1941, I. Gelfand proved that if a is a doubly power-bounded element of a Banach algebra A such that Sp(a) = 1, then a = 1. In [4], this result has been extended locally to a larger class of operators. In this note, we first give some quantitative local extensions of Gelfand-Hille’s results. Secondly, using the Bernstein inequality for multivariable functions, we give short and elementary proofs of two extensions of Gelfand’s theorem for m commuting bounded operators, , on a Banach space X.
Fernando Cobos (1988)
Colloquium Mathematicae
S. Kwapień (1970)
Studia Mathematica
R.A. Lorentz, W.P. Kamp, P.A. Rejto (1989)
Journal für die reine und angewandte Mathematik
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....
Manuel A. Fugarolas (2011)
Czechoslovak Mathematical Journal
Let and . We prove that , the ideal of operators of Geľfand type , is contained in the ideal of -absolutely summing operators. For this generalizes a result of G. Bennett given for operators on a Hilbert space.
Andrzej Pokrzywa (1994)
Banach Center Publications
Wolfgang Lusky (1998)
Acta Universitatis Carolinae. Mathematica et Physica
N. J. Nielsen (1973)
Ed Dubinsky, A. Pełczyński, H. Rosenthal (1972)
Studia Mathematica
Jesús M. Martínez Castillo (1995)
Extracta Mathematicae
M.A. Fugarolas (1984)
Monatshefte für Mathematik
Eve Oja (2010)
Banach Center Publications
This survey features some recent developments concerning the bounded approximation property in Banach spaces. As a central theme, we discuss the weak bounded approximation property and the approximation property which is bounded for a Banach operator ideal. We also include an overview around the related long-standing open problem: Is the approximation property of a dual Banach space always metric?
Krzysztof Nowak (1993)
Monatshefte für Mathematik
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