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On group representations whose C * algebra is an ideal in its von Neumann algebra

Edmond E. Granirer (1979)

Annales de l'institut Fourier

Let τ be a continuous unitary representation of the locally compact group G on the Hilbert space H τ . Let C τ * [ V N τ ] be the C * [ W * ] algebra generated by ( L 1 ( G ) ) and M τ ( C τ * ) = φ V N τ ; φ C τ * + C τ * φ C τ * . The main result obtained in this paper is Theorem 1:If G is σ -compact and M τ ( C τ * ) = V N τ then supp τ is discrete and each π in supp τ in CCR.We apply this theorem to the quasiregular representation τ = π H and obtain among other results that M π H ( C π H * ) = V N π H implies in many cases that G / H is a compact coset space.

On Hamel bases in Banach spaces

Juan Carlos Ferrando (2014)

Studia Mathematica

It is shown that no infinite-dimensional Banach space can have a weakly K-analytic Hamel basis. As consequences, (i) no infinite-dimensional weakly analytic separable Banach space E has a Hamel basis C-embedded in E(weak), and (ii) no infinite-dimensional Banach space has a weakly pseudocompact Hamel basis. Among other results, it is also shown that there exist noncomplete normed barrelled spaces with closed discrete Hamel bases of arbitrarily large cardinality.

On Hankel transform and Hankel convolution of Beurling type distributions having upper bounded support

M. Belhadj, Jorge J. Betancor (2004)

Czechoslovak Mathematical Journal

In this paper we study Beurling type distributions in the Hankel setting. We consider the space ( w ) ' of Beurling type distributions on ( 0 , ) having upper bounded support. The Hankel transform and the Hankel convolution are studied on the space ( w ) ' . We also establish Paley Wiener type theorems for Hankel transformations of distributions in ( w ) ' .

On having a countable cover by sets of small local diameter

Nadezhda Ribarska (2000)

Studia Mathematica

A characterization of topological spaces admitting a countable cover by sets of small local diameter close in spirit to known characterizations of fragmentability is obtained. It is proved that if X and Y are Hausdorff compacta such that C(X) has an equivalent p-Kadec norm and C p ( Y ) has a countable cover by sets of small local norm diameter, then C p ( X × Y ) has a countable cover by sets of small local norm diameter as well.

Currently displaying 461 – 480 of 1948