In this paper we consider the similarity problem for A(G): Is every bounded representation of A(G) on a Hilbert space H similar to a *-representation?
We prove that if T is a strongly based continuous bounded representation of a locally compact abelian group G on a Banach Space X, and if the spectrum of T is countable, then the Banach algebra generated by f̂ (T) = ∫Gf(g) T g) dg, f ∈ L1(G), is semisimple.
We prove a theorem of Dixmier and Malliavin type for analytic vectors of bounded representations of (R,+): Let (π,E) be a bounded representation of (R,+) in a Banach space E and let A be the convolution algebra of analytic vectors for the left regular representation of R on L1(R), then A∗A="A and π(A E="Eω.
Such problems are studied for strongly continuous bounded representations of locally compact, abelian semigroups of linear operators on Banach spaces.
Let S be a locally compact abelian semigroup and T a bounded representation of S by linear bounded operators in a Banach space X, with spectrum Sp(T).
The same is proved for the space of unital ultraweakly continuous bounded representations from an injective von Neumann algebra M into N.
We characterize groups with Guoliang Yuʼs property A (i.e., exact groups) by the existence of a family of uniformly bounded representations which approximate the trivial representation.
We show that for each strongly continuous, uniformly bounded representation R of G in a UMD space X, there is a corresponding direct-sum decomposition of X which reflects the order in Ĝ.
It is also possible that the bound representation of shape and color forms a unified structure that is stored as a unit of information in the memory and, therefore, cannot be divided or suppressed (Morey 2009).
The creation of temporary bound representation of information from different sources is one of the key abilities attributed to the episodic buffer component of working memory.
