scholarly journals Product formula for nonlinear semigroups in Hilbert spaces

1982 ◽  
Vol 58 (10) ◽  
pp. 425-428 ◽  
Author(s):  
Yoshikazu Kobayashi
Keyword(s):  
Hilbert Spaces ◽  
Product Formula ◽  
Nonlinear Semigroups

scholarly journals A COMPLETELY ENTANGLED SUBSPACE OF MAXIMAL DIMENSION

2006 ◽  
Vol 04 (02) ◽  
pp. 325-330 ◽  
Author(s):  
B. V. RAJARAMA BHAT
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Product Formula ◽  
Maximal Dimension ◽  
Maximum Dimension ◽  
Dimension Formula ◽  
Finite Dimensional ◽  
Minimum Dimension ◽  
Orthogonal Product ◽  
Product Vector

Consider a tensor product [Formula: see text] of finite-dimensional Hilbert spaces with dimension [Formula: see text], 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of [Formula: see text] with no non-zero product vector is known to be d1 d2…dk - (d1 + d2 + … + dk + k - 1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and show that it has the minimum dimension possible for an unextendible product basis of not necessarily orthogonal product vectors.

scholarly journals Infinite symmetric group, pseudomanifolds, and combinatorial cobordism-like structures

2018 ◽  
Vol 10 (03) ◽  
pp. 605-625 ◽  
Author(s):  
Alexander A. Gaifullin ◽  
Yury A. Neretin
Keyword(s):  
Symmetric Group ◽  
Hilbert Spaces ◽  
Double Coset ◽  
Product Formula ◽  
Linear Operators ◽  
The Other ◽  
Unitary Representations ◽  
Infinite Symmetric Group ◽  
Bounded Linear ◽  
Coset Spaces

We consider a category [Formula: see text] whose morphisms are [Formula: see text]-dimensional pseudomanifolds equipped with certain additional structures (coloring and labeling of some cells), multiplication of morphisms is similar to a concatenation of cobordisms. On the other hand, we consider the product [Formula: see text] of [Formula: see text] copies of infinite symmetric group. We construct a correspondence between the sets of morphisms of [Formula: see text] and double coset spaces of [Formula: see text] with respect to certain subgroups. We show that unitary representations of [Formula: see text] produce functors from the category of [Formula: see text] to the category of Hilbert spaces and bounded linear operators.

scholarly journals Commutativity of the Haagerup tensor product and base change for operator modules

2021 ◽  
pp. 1-11
Author(s):  
Tyrone Crisp
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Base Change ◽  
Product Formula ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Continuous Mappings ◽  
Continuous Fields ◽  
Bounded Norm

By computing the completely bounded norm of the flip map on the Haagerup tensor product [Formula: see text] associated to a pair of continuous mappings of locally compact Hausdorff spaces [Formula: see text], we establish a simple characterization of the Beck-Chevalley condition for base change of operator modules over commutative [Formula: see text]-algebras, and a descent theorem for continuous fields of Hilbert spaces.

scholarly journals A Modified Approach to the Doplicher/Roberts Theorem on the Construction of the Field Algebra and the Symmetry Group in Superselection Theory

1997 ◽  
Vol 09 (03) ◽  
pp. 279-313 ◽  
Author(s):  
H. Baumgärtel
Keyword(s):  
Symmetry Group ◽  
Hilbert Spaces ◽  
Product Formula ◽  
Full System ◽  
Field Algebra ◽  
C Algebra ◽  
Starting Point ◽  
Trivial Center ◽  
Algebraic Formula ◽  
Fixed Point Algebra

Let [Formula: see text] be a unital C*-algebra with trivial center [Formula: see text]. Let [Formula: see text] denote a tensorial category of unital endomorphisms of [Formula: see text] equipped with several properties to be explained in the text. Doplicher and Roberts have shown, among other things, that there is a C*-algebra [Formula: see text] and a compact group [Formula: see text] of automorphisms of ℱ such that ℱ is a Hilbert C*-system over [Formula: see text] w.r.t. [Formula: see text], where [Formula: see text] is the fixed point algebra w.r.t. [Formula: see text], [Formula: see text] and the objects [Formula: see text] are characterized as the canonical endomorphisms of certain algebraic [Formula: see text]-invariant Hilbert spaces ℋρ⊂ℱ, see Doplicher/Roberts [1, 2, 3]. The starting point of the approach presented in this paper to point out the mentioned result is an [Formula: see text]-leftmodule ℱ0:={∑ρ,jAρ,jΦρ,j}. ρ runs through a full system of irreducible and mutually disjoint objects of [Formula: see text], j=1,2,…,d(ρ), where d(ρ) denotes the statistical dimension of [Formula: see text] is an orthonormal basis of a d(ρ)-dimensional Hilbert space. The system {Φρj}ρj forms a leftmodule basis of ℱ0, the coefficients Aρj are members of [Formula: see text]. The strategy is to equip successively ℱ0 with a bimodule structure, a product and a *-structure and finally with a C*-norm ||.||*. The symmetry group [Formula: see text] appears as the group of all automorphisms of the *-algebra ℱ0 leaving the [Formula: see text]-scalar product [Formula: see text] invariant, where F=∑ρ,jAρjΦρj, G=∑ρ,jBρjΦρj. The field algebra is then given by ℱ:= clo ||.||*ℱ0.

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