Displaying similar documents to “A density theorem for F-spaces”

A density theorem for algebra representations on the space (s)

W. Żelazko (1998)

Studia Mathematica

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We show that an arbitrary irreducible representation T of a real or complex algebra on the F-space (s), or, more generally, on an arbitrary infinite (topological) product of the field of scalars, is totally irreducible, provided its commutant is trivial. This provides an affirmative solution to a problem of Fell and Doran for representations on these spaces.

An example of a generalized completely continuous representation of a locally compact group

Detlev Poguntke (1993)

Studia Mathematica

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There is constructed a compactly generated, separable, locally compact group G and a continuous irreducible unitary representation π of G such that the image π(C*(G)) of the group C*-algebra contains the algebra of compact operators, while the image π ( L 1 ( G ) ) of the L 1 -group algebra does not containany nonzero compact operator. The group G is a semidirect product of a metabelian discrete group and a “generalized Heisenberg group”.

Recent developments in hypercyclicity.

Karl-Goswin Grosse-Erdmann (2003)

RACSAM

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In these notes we report on recent progress in the theory of hypercyclic and chaotic operators. Our discussion will be guided by the following fundamental problems: How do we recognize hypercyclic operators? How many vectors are hypercyclic? How many operators are hypercyclic? How big can non-dense orbits be?

Some Ramsey type theorems for normed and quasinormed spaces

C. Henson, Nigel Kalton, N. Peck, Ignác Tereščák, Pavol Zlatoš (1997)

Studia Mathematica

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We prove that every bounded, uniformly separated sequence in a normed space contains a “uniformly independent” subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in L p [ 0 , 1 ] for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.