arXiv subjects

G. K. Eleftherakis

Publications and source records attributed to G. K. Eleftherakis.

23 records · Page 2Linked to original sources

arXiv2011

Ranges of bimodule projections and reflexivity

We develop a general framework for reflexivity in dual Banach spaces, motivated by the question of when the weak* closed linear span of two reflexive masa-bimodules is automatically reflexive. We establish an affirmative answer to this question in a number of cases by examining two new classes of masa-bimodules, defined in terms of ranges of masa-bimodule projections. We give a number of corollaries of our results concerning operator and spectral synthesis, and show that the classes of masa-bimodules we study are operator synthetic if and only if they are strong operator Ditkin.

math.OA↗

arXiv2010

Morita equivalence of nest algebras

Let N_1 (resp.N_2) be a nest A (resp. B) be the corresponding nest algebra, A_0 (resp. B_0) be the subalgebra of compact operators. We prove that the nests N_1, N_2 are isomorphic if and only if the algebras A, B are weakly-* Morita equivalent if and only if the algebras A_0, B_0 are strongly Morita equivalent. We characterize the nest isomorphisms which implement stable isomorphism between the corresponding nest algebras.

math.OA↗

arXiv2008

Stable isomorphism of dual operator spaces

We prove that two dual operator spaces $X$ and $Y$ are stably isomorphic if and only if there exist completely isometric normal representations $ϕ$ and $ψ$ of $X$ and $Y$, respectively, and ternary rings of operators $M_1, M_2$ such that $ϕ(X)= [M_2^*ψ(Y)M_1]^{-w^*}$ and $ψ(Y)=[M_2ϕ(X)M_1^*].$ We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic. We apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic. We provide examples motivated by CSL algebra theory.

math.OA↗

arXiv2007

Morita Type Equivalences and Reflexive Algebras

Two unital operator algebras A, B are called Delta-equivalent if there exists an equivalence functor between the categories A-mod and B-mod which "extends" to a *-functor implementing an equivalence between the categories A-dmod and B-dmod. Here A-mod denotes the category of normal representations of A and A-dmod denotes the category with the same objects as A-mod and D(A)-module maps (D(A) is the diagonal of A). We prove that any such functor maps completely isometric representations to completely isometric representations, "respects" the lattices of the algebras and maps reflexive algebras to reflexive algebras. We present applications to the class of CSL algebras.

math.OA↗

arXiv2007

A Morita Type Equivalence for Dual Operator Algebras

We generalize the main theorem of Rieffel for Morita equivalence of W*-algebras to the case of unital dual operator algebras: two unital dual operator algebras A and B have completely isometric normal representations alpha, beta such that alpha(A) is the w*-closed span of M*beta(B)M and beta(B) is the w*-closed span of Malpha(A)M* for a ternary ring of operators M (i.e. a linear space M such that MM*M \subset M if and only if there exists an equivalence functor $F:_{A}M\to_{B}M$ which "extends" to a *-functor implementing an equivalence between the categories $_{A}DM$ and $_{B}DM.$ By $_{A}M$ we denote the category of normal representations of A and by $_{A}DM$ the category with the same objects as $_{A}M$ and $Δ(A)$-module maps as morphisms ($Δ(A)=A\cap A^*$). We prove that this functor is equivalent to a functor "generated" by a B, A bimodule, that it is normal and completely isometric.

math.OA↗