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We define a relation < for dual operator algebras. We say that B < A if there exists a projection p in A such that B and pAp are Morita equivalent in our sense. We show that < is transitive, and we investigate the following question: If A < B and B < A, then is it true that A and B are stably isomorphic? We propose an analogous relation < for dual operator spaces, and we present some properties of < in this case.
We introduce a Morita type equivalence: two operator algebras $A$ and $B$ are called strongly $Delta $-equivalent if they have completely isometric representations $alpha $ and $beta $ respectively and there exists a ternary ring of operators $M$ suc
We introduce the notion of $Delta$ and $sigma,Delta-$ pairs for operator algebras and characterise $Delta-$ pairs through their categories of left operator modules over these algebras. Furthermore, we introduce the notion of $Delta$-Morita equivalent
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar multipliers of a
In this paper, two related types of dualities are investigated. The first is the duality between left-invertible operators and the second is the duality between Banach spaces of vector-valued analytic functions. We will examine a pair ($mathcal{B},Ps
We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to