This paper continues the investigation of the rst author begun in part one. The hereditary properties of n-homomorphism amenability for Banach algebras are investigated and the relations between n-homomorphism amenability of a Banach algebra and its ideals are found. Analogous to the character amenability, it is shown that the tensor product of two unital Banach algebras is n-homomorphism amena...

We study the range transformations 0p(/fD, Reß) and Op(/fD, B) for Banach function algebras A and B. As a special instance, the harmonicity of functions in Op(/fD, Re A) for a nontrivial function algebra A is established and is compared with previous investigations of Op( An, A) and Op((Re/l);, (Re/1)) for an interval /. In §2 we present some results on Op(AD, B) and use them to show that funct...

Let AI, be commutative semlslmple Banach algebras and 1 02 A2 be their projective tensor product. We prove that, if 10 2 is a group algebra (measure algebra) of a locally compact abelian group, then so are A 1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutatlve semi-simple Banach algebra, then the Banach algebra LI(G,A) of A-valued Bochner inte...

In this paper, we introduce an algebra of singular integral operators containing Bessel potentials of positive order, and show that the corresponding unital Banach algebra is an inverseclosed Banach subalgebra of B(Lw), the Banach algebra of all bounded operators on the weighted space Lw, for all 1 ≤ q < ∞ and Muckenhoupt Aq-weights w. Mathematics Subject Classification (2000) 47L80, 42B20, 45P...

We investigate possible preduals of the measure algebra M(G) of a locally compact group and the Fourier algebra A(G) of a separable compact group. Both of these algebras are canonically dual spaces and the canonical preduals make the multiplication separately weak∗-continuous so that these algebras are dual Banach algebras. In this paper we find additional conditions under which the preduals C0...

We establish triviality of some holomorphic Banach vector bundles on the maximal ideal space M(H∞) of the Banach algebra H∞ of bounded holomorphic functions on the unit disk D ⊂ C with pointwise multiplication and supremum norm. We apply the result to the study of the Sz.-Nagy operator corona problem. 1. Formulation of Main Results 1.1. We continue our study started in [Br2] of analytic objects...

Introduction. A great deal of work has been done in the last fifteen years on the theory and classification of irreducible unitary representations of locally compact groups. It is also generally recognized (see for example [12, § 8]) that, at least for some classes of groups, it is artificial to confine oneself to unitary representations; one ought to study the irreducible Banach space represen...

for two algebras $a$ and $b$, a linear map $t:a longrightarrow b$ is called separating, if $xcdot y=0$ implies $txcdot ty=0$ for all $x,yin a$. the general form and the automatic continuity of separating maps between various banach algebras have been studied extensively. in this paper, we first extend the notion of separating map for module case and then we give a description of a linear separa...

Let $A$ be a Banach algebra, $\Omega(A)$ be the character space of $A$ and $\alpha\in\Omega(A)$. In this paper, we examine the characteristics of $\alpha$-projective (injective) $A$-modules and demonstrate that these character-based $A$-modules also satisfy well-known classical homological properties on Banach $A$-modules.

Let A be a dual Banach algebra with predual A∗ and consider the following assertions: (A) A is Connes-amenable; (B) A has a normal, virtual diagonal; (C) A∗ is an injective A-bimodule. For general A, all that is known is that (B) implies (A) whereas, for von Neumann algebras, (A), (B), and (C) are equivalent. We show that (C) always implies (B) whereas the converse is false for A = M(G) where G...