Let A be an associative algebra over a field F of characteristic zero and let L Lie F. If acts on by derivations, then such action determines its universal enveloping U(L) in this case we refer to as with derivations or L-algebra. Here give characterization the ideal differential identities finite dimensional L-algebras corresponding sequence codimensions ${c_{n}^{L}} (A)$ , n ≥ 1, is polynomia...

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...

We introduce the concept of reflexivity for bounded n-linear maps and investigate the reflexivity of Zn(L1(G),X), the space of bounded ncocycles from L1(G)(n) into X, where L1(G) is the group algebra of a locally compact group G and X is a Banach L1(G)-bimodule. We show that Zn(L1(G), X) is reflexive for a large class of groups including groups with polynomial growth, IN-groups, maximally almos...

Abstract. We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A1 and A2 are operator algebras, then any bounded epimorphism of A1 onto A2 is completely bounded provided that A2 contains a norming C ∗-subalgebra. We use this result to give some insights into Kadison’s Similarity Problem: we show that every faithful bounded homomo...

We present an intrinsically defined algebra of operators containing the right and left invariant Calderón-Zygmund operators on a stratified group. The operators in our algebra are pseudolocal and bounded on Lp (1 < p <∞). This algebra provides an example of an algebra of singular integrals that falls outside of the classical Calderón-Zygmund theory.

Non-commutative L-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algeb...

We introduce a new concept of the bounded rank (with respect to a positive constant) for unital C∗-algebras as a modification of the usual real rank. We present a series of conditions insuring that bounded and real ranks coincide. These observations are then used to prove that for a given n and K > 0 there exists a separable unital C∗-algebra Z n such that every other separable unital C∗-algebr...

Introduction. I t is known [13] that a Lie algebra over a modular field has indecomposable representations of arbitrarily high dimensionalities. If, however, the Lie algebra and its representations are required to be restricted (see [6, Chapter 5] for definitions), this need no longer be the case. A restricted Lie algebra for which the degrees of its (restricted) indecomposable representations ...

We classify the Harish-Chandra modules over the higher rank Virasoro and super-Virasoro algebras: It is proved that a Harish-Chandra module, i.e., an irreducible weight module with finite weight multiplicities, over a higher rank Virasoro or super-Virasoro algebra is a module of the intermediate series. As an application, it is also proved that an indecomposable weight module with finite weight...

The notation and terminology used in this paper are introduced in the following articles: [2], [16], [9], [14], [7], [8], [3], [18], [17], [4], [19], [5], [15], [1], [20], [12], [11], [10], [21], [13], and [6]. Let V be a complex algebra. A complex algebra is called a complex subalgebra of V if it satisfies the conditions (Def. 1). (Def. 1)(i) The carrier of it ⊆ the carrier of V , (ii) the add...