Spectral theory and hypercyclic subspaces

DOI10.1090/S0002-9947-00-02743-4zbMath0961.47003OpenAlexW2169260460MaRDI QIDQ4510032

Fernando León-Saavedra, Alfonso Montes-Rodríguez

Publication date: 19 October 2000

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02743-4

zbMATH Keywords

essential spectrummultipliercomposition operatorhypercyclic operatorbackward shiftHilbert spaces of entire functionsdifferentiation operatortranslation operatorbilateral shiftessential minimum modulus

Mathematics Subject Classification ID

Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) (Semi-) Fredholm operators; index theories (47A53) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Linear composition operators (47B33) Cyclic vectors, hypercyclic and chaotic operators (47A16)

Related Items

Hypercyclic subspaces in omega, Universal families and hypercyclic operators, On the set of hypercyclic vectors for the differentiation operator, Algebrable sets of hypercyclic vectors for convolution operators, Structure of sets of bounded sequences with a prescribed number of accumulation points, Hypercyclic subspaces and weighted shifts, Explicit constructions of dense common hypercyclic subspaces, Existence of common and upper frequently hypercyclic subspaces, Frequently hypercyclic subspaces, Hypercyclic subspaces for Fréchet space operators, Backward \(\varPhi\)-shifts and universality, Supercyclic subspaces: Spectral theory and weighted shifts, Universal Taylor series with maximal cluster sets, Extended abstract theory of universal series and applications, Hereditarily hypercylic operators, Linear subsets of nonlinear sets in topological vector spaces

Cites Work

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• On the invariant subspace problem for Banach spaces
• Limits of hypercyclic and supercyclic operators
• Composition operators and classical function theory
• Linear structure of hypercyclic vectors
• The surjectivity radius, packing numbers and boundedness below of linear operators
• Hypercyclic and cyclic vectors
• Non-finite dimensional closed vector spaces of universal functions for composition operators
• Sequences of derivatives and normal families
• Cyclic phenomena for composition operators
• A Solution to the Invariant Subspace Problem on the Space l ₁
• Universal Vectors for Operators on Spaces of Holomorphic Functions
• A Metatheorem on Similarity and Approximation of Operators
• A Hypercyclic Operator whose Adjoint is Also Hypercyclic
• Invariant Manifolds of Hypercyclic Vectors
• Hypercyclic Weighted Shifts
• On orbits of elements
• On approximation by euclidean and non-euclidean translations of an analytic function
• Banach spaces of hypercyclic vectors