Toeplitz operators related to certain domains in
J. Janas (1975)
Studia Mathematica
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J. Janas (1975)
Studia Mathematica
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Heinz O. Cordes (1986)
Revista Matemática Iberoamericana
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Iain Raebum (1978)
Studia Mathematica
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Albrecht Böttcher, Hartmut Wolf (1997)
Banach Center Publications
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Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk or on the Segal-Bargmann space over . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression of A to the linear span of the monomials . Unfortunately, in general the spectrum of does not mimic the spectrum...
L. A. Coburn, R. G. Douglas (1971)
Publications Mathématiques de l'IHÉS
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A. Dash (1973)
Studia Mathematica
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Derek Kitson (2009)
Studia Mathematica
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We extend the notion of ascent and descent for an operator acting on a vector space to sets of operators. If the ascent and descent of a set are both finite then they must be equal and give rise to a canonical decomposition of the space. Algebras of operators, unions of sets and closures of sets are treated. As an application we construct a Browder joint spectrum for commuting tuples of bounded operators which is compact-valued and has the projection property.
Matej Brešar, Yuri V. Turovskii (2007)
Studia Mathematica
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Various topics concerning compact elementary operators on Banach algebras are studied: their ranges, their coefficients, and the structure of algebras having nontrivial compact elementary operators. In the first part of the paper we consider separately elementary operators of certain simple types. In the second part we obtain our main results which deal with general elementary operators.
Weis, L. W.
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