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Topological properties in tensor products of Banach spaces [PDF]
Journal of Functional Analysis, 2022 Given two Banach spaces $X$ and $Y$, we analyze when the projective tensor product $X\widehat{\otimes}_ Y$ has Corson's property (C) or is weakly Lindel f determined (WLD), subspace of a weakly compactly generated (WCG) space or subspace of a Hilbert generated space. For instance, we show that: (i) $X\widehat{\otimes}_ Y$ is WLD if and only if both $
Antonio Avilés +3 more
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Compactness in Topological Tensor Products and Operator Spaces [PDF]
Proceedings of the American Mathematical Society, 1972 Let E and F be Banach spaces, E(?F their algebraic tensor product, and E (?,a F the completion of E(?F with respect to a uniform crossnorm oc?i (where ) is the "least", and y the greatest, crossnorm). In ?2 we characterize the relatively compact subsets of E (DA Fas those which, considered as spaces of operators from E* to F and from F* to E, take the ...
J. R. Holub
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A survey on duals of topological tensor products [PDF]
Rendiconti del Seminario Matematico, 2016 We give a survey on classical and recent results on dual spaces of topological tensor products as well as some examples where these are used.
Eduard A. Nigsch, Norbert Ortner
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On topological tensor products of functional Fréchet and DF spaces [PDF]
Integral Transforms and Special Functions, 2009 A convenient technique for calculating completed topological tensor products of functional Frechet and DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire analytic functions.
A. G. Smirnov
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Tensor product representation of a topological ordered phase: Necessary symmetry conditions [PDF]
Physical Review B, 2010 The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional methods due to their long range entanglement. However, an important issue arises when we use tensor product states (TPS)
Isaac L. Chuang +4 more
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Topological Tensor Products of Unbounded Operator Algebras on Frechet Domains
Publications of the Research Institute for Mathematical Sciences, 1997 The aim of this paper is to investigate topological properties of unbounded operator algebras \mathcal A⊂L^+(D) and its stability under the formation of topological tensor products \mathcal A_1 \otimes_ ...
Wolf‐Dieter Heinrichs
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Topological tensor product of bimodules, complete Hopf algebroids and convolution algebras [PDF]
Communications in Contemporary Mathematics, 2018 Given a finitely generated and projective Lie–Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids between the completion of the finite dual of its universal enveloping Hopf algebroid and the associated convolution algebra. The topological Hopf algebroid structure of this convolution algebra is here
Laiachi El Kaoutit, Paolo Saracco
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Hochschild cohomology of tensor products of topological algebras [PDF]
Proceedings of the Edinburgh Mathematical Society, 2010 AbstractWe describe explicitly the continuous Hochschild and cyclic cohomology groups of certain tensor products of $\widehat{\otimes}$-algebras which are Fréchet spaces or nuclear DF-spaces. To this end we establish the existence of topological isomorphisms in the Künneth formula for the cohomology of complete nuclear DF-complexes and in the Künneth ...
Zinaida A. Lykova
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SOME ALGEBRAIC AND TOPOLOGICAL PROPERTIES OF THE NONABELIAN TENSOR PRODUCT [PDF]
Bulletin of the Korean Mathematical Society, 2013 Several authors investigated the properties which are invariant under the passage from a group to its nonabelian tensor square. In the present note we study this problem from the viewpoint of the classes of groups and the methods allow us to prove a result of invariance for some geometric properties of discrete groups.
Daniele Ettore Otera +2 more
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Heredity of Tensor Products of Topological Algebras
Mathematische Annalen, 1966 The purpose of the present paper is to put into the context of the theory of tensor products of topological algebras [9], [10] some recent results concerning certain properties of permanence of a tensor product of Banach algebras [4], [5]. A brief report of the main results of this paper has been given in [11].
Anastasios Mallios
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