Displaying similar documents to “A perturbation of Lomonosov's theorem”

An introduction to Rota’s universal operators: properties, old and new examples and future issues

Carl C. Cowen, Eva A. Gallardo-Gutiérrez (2016)

Concrete Operators

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The Invariant Subspace Problem for Hilbert spaces is a long-standing question and the use of universal operators in the sense of Rota has been an important tool for studying such important problem. In this survey, we focus on Rota’s universal operators, pointing out their main properties and exhibiting some old and recent examples.

On class A operators

Sungeun Jung, Eungil Ko, Mee-Jung Lee (2010)

Studia Mathematica

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We show that every class A operator has a scalar extension. In particular, such operators with rich spectra have nontrivial invariant subspaces. Also we give some spectral properties of the scalar extension of a class A operator. Finally, we show that every class A operator is nonhypertransitive.

On w-hyponormal operators

Eungil Ko (2003)

Studia Mathematica

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We study some properties of w-hyponormal operators. In particular we show that some w-hyponormal operators are subscalar. Also we state some theorems on invariant subspaces of w-hyponormal operators.

On invariant subspaces for polynomially bounded operators

Junfeng Liu (2017)

Czechoslovak Mathematical Journal

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We discuss the invariant subspace problem of polynomially bounded operators on a Banach space and obtain an invariant subspace theorem for polynomially bounded operators. At the same time, we state two open problems, which are relative propositions of this invariant subspace theorem. By means of the two relative propositions (if they are true), together with the result of this paper and the result of C. Ambrozie and V. Müller (2004) one can obtain an important conclusion that every polynomially...

Narrow operators and rich subspaces of Banach spaces with the Daugavet property

Vladimir M. Kadets, Roman V. Shvidkoy, Dirk Werner (2001)

Studia Mathematica

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Let X be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on X which depend only on the norms of the images of elements. This approach is applied to the Daugavet equation for norms of operators; in particular we develop a general theory of narrow operators and rich subspaces of spaces X with the Daugavet property previously studied in the context of the classical spaces C(K) and L₁(μ).

Quasireducible operators.

Kubrusly, C. S. (2003)

International Journal of Mathematics and Mathematical Sciences

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Intertwining Multiplication Operators on Function Spaces

Bahman Yousefi, Leila Bagheri (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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Suppose that X is a Banach space of analytic functions on a plane domain Ω. We characterize the operators T that intertwine with the multiplication operators acting on X.