We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and ...the entire space of matrices of a given size. The construction uses twisted tensor products and their deformations combined with invariance properties derived from quantum symmetric pairs. These quantum Weyl algebras admit Uq(glN)-module algebra structures compatible with standard ones on the polynomial part, have relations that are expressed nicely via matrices, and are closely related to an algebra arising in the theory of quantum bounded symmetric domains.
Szlenk index of C ( K ) ⊗ ˆ π C ( L ) Causey, R.M.; Galego, E.M.; Samuel, C.
Journal of functional analysis,
05/2022, Volume:
282, Issue:
9
Journal Article
Let M be a von Neumann algebra equipped with a normal semi-finite faithful trace (nsf trace in short) and let T:M→M be a contraction. We say that T is absolutely dilatable if there exist another von ...Neumann algebra M′ equipped with a nsf trace, a w⁎-continuous trace preserving unital ⁎-homomorphism J:M→M′ and a trace preserving ⁎-automorphism U:M′→M′ such that Tk=EUkJ for all integer k≥0, where E:M′→M is the conditional expectation associated with J. Given a σ-finite measure space (Ω,μ), we characterize bounded Schur multipliers ϕ∈L∞(Ω2) such that the Schur multiplication operator Tϕ:B(L2(Ω))→B(L2(Ω)) is absolutely dilatable. In the separable case, they are characterized by the existence of a von Neumann algebra N with a separable predual, equipped with a normalized normal faithful trace τN, and a w⁎-measurable essentially bounded function d:Ω→N such that ϕ(s,t)=τN(d(s)⁎d(t)) for almost every (s,t)∈Ω2.
We link conditional weak mixing and ergodicity via the tensor product in Riesz spaces. In particular, we characterise conditional weak mixing of a conditional expectation preserving system by the ...ergodicity of its tensor product with itself or other ergodic systems. Along the way we characterise components of weak order units in the tensor product space in terms of tensor products of components of weak order units.
In this paper, we prove that if Cohen–Macaulay local/graded rings A, B and R satisfy certain conditions regarding multiplicity and Cohen–Macaulay type, then almost Gorenstein property of R implies ...Gorenstein properties for all of A, B and R. We apply our theorem to tensor products of semi-standard graded rings and some classes of affine semigroup rings, i.e., numerical semigroup rings, edge rings and stable set rings.
We prove that if a metric space M has the finite CEP then F(M)⊗ˆπX has the Daugavet property for every non-zero Banach space X. This applies, for instance, if M is a Banach space whose dual is ...isometrically an L1(μ) space. If M has the CEP then L(F(M),X)=Lip0(M,X) has the Daugavet property for every non-zero Banach space X, showing that this is the case when M is an injective Banach space or a convex subset of a Hilbert space.
For a given discrete group G, we apply results of Kirchberg on exact and injective tensor products of C^*-algebras to give an explicit description of the minimal exact correspondence crossed-product ...functor and the maximal injective crossed-product functor for G in the sense of Buss, Echterhoff and Willett. In particular, we show that the former functor dominates the latter.
We continue our study of tensor products in the operator system category. We define operator system quotients and exactness in this setting and refine the notion of nuclearity by studying operator ...systems that preserve various pairs of tensor products. One of our main goals is to relate these refinements of nuclearity to the Kirchberg conjecture. In particular, we prove that the Kirchberg conjecture is equivalent to the statement that every operator system that is (min,er)-nuclear is also (el,c)-nuclear. We show that operator system quotients are not always equal to the corresponding operator space quotients and then study exactness of various operator system tensor products for the operator system quotient. We prove that an operator system is exact for the min tensor product if and only if it is (min,el)-nuclear. We give many characterizations of operator systems that are (min,er)-nuclear, (el,c)-nuclear, (min,el)-nuclear and (el,max)-nuclear. These characterizations involve operator system analogues of various properties from the theory of C*-algebras and operator spaces, including the WEP and LLP.
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