Advanced Operator Algebra Research

The preduals of $W^*$-algebras are 1-Plichko spaces. A natural question arises: does every predual possess a projectional skeleton (PS) $\{P_s:s\in J\}$ such that each $P_s^*$ is a conditional expectation? In this note, we answer this question affirmatively for the preduals of the group von Neumann algebras of locally…

The preduals of $W^*$-algebras are 1-Plichko spaces. A natural question arises: does every predual possess a projectional skeleton (PS) $\{P_s:s\in J\}$ such that each $P_s^*$ is a conditional expectation? In this note, we answer this question affirmatively for the preduals of the group von Neumann algebras of locally…

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Abstract In this paper, we introduce a simplicial analog of classifying spaces for commutativity which classify principal bundles with commutativity structure on their transition functions. Our construction $$\overline{W}(\tau ,K)$$ W ¯ ( τ , K ) , which takes as input a simplicial group K and a cosimplicial group $$\…

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We prove results for Leavitt path algebras with coefficients in a unital commutative ring most of which are new for field coefficients also. In particular, we show that the ideal lattice of a Leavitt path algebra embeds into the ideal lattice of the path algebra of the same digraph. As a consequence we provide a conve…

We show that compactness of orthogonally additive operators between Banach lattices is not preserved under taking the modulus by providing a nonlinear analogue of Krengel’s example. In contrast, for operators acting from a Banach lattice into an AM-space, AM-compactness is stable under lattice operations. Moreover, th…

We introduce the \emph{tame factorization property} for triples of Fréchet spaces: a triple $(E,G,F)$ has the tame factorization property, denoted by $(E,G,F) \in \mathfrak{TF}$, if there exists a nondecreasing function $S:\mathbb{N}\to\mathbb{N}$ such that every operator from $E$ to $F$ factoring through $G$ is $S$-t…

This paper explores actor structures in group-groupoids, using the Brown-Spencer theorem to establish actors as universal objects and split extension classifiers. We construct the center and commutator subgroup of a group-groupoid, revealing their roles in internal symmetries, and introduce the holomorph as a categori…

Motivated by the simplification of decomposition formulas for fibred bisets, we study the homomorphism extension problem for subdirect products of finite groups when the codomain is an abelian group satisfying certain hypothesis. We prove that every homomorphism of subdirect products whose Goursat quotients have trivi…

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An R -module M is said to be a semisimple-continuous, if it is weak 𝐶𝑆 (i.e., every semisimple submodule of M is essential in a direct summand of M ) and semisimple-direct injective (i.e., if A and B are isomorphic semisimple submodules of M such that A is a direct summand of M , then B is a direct summand of M ). It…

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