scholarly journals SPECTRAL THEORY, TENSOR PRODUCTS AND INFINITE DIMENSIONAL HOLOMORPHY

2004 ◽  
Vol 41 (1) ◽  
pp. 193-207 ◽  
Author(s):  
Sean Dineen
Keyword(s):  
Spectral Theory ◽  
Tensor Products ◽  
Infinite Dimensional ◽  
Infinite Dimensional Holomorphy

Simple Cn modules with multiplicities 1 and applications

1994 ◽  
Vol 72 (7-8) ◽  
pp. 326-335 ◽  
Author(s):  
D. J. Britten ◽  
J. Hooper ◽  
F. W. Lemire
Keyword(s):  
Weyl Group ◽  
Tensor Products ◽  
Weight Space ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Recursion Formulas ◽  
Completely Reducible ◽  
Index 2

In this paper we show that there exist exactly two nonequivalent simple infinite dimensional highest weight Cn modules having the property that every weight space is one dimensional. The tensor products of these modules with any finite-dimensional simple Cn module are proven to be completely reducible and we provide an explicit decomposition for such tensor products. As an application of these decompositions, we obtain two recursion formulas for computing the multiplicities of simple finite dimensional Cn modules. These formulas involve a sum over subgroups of index 2 in the Weyl group of Cn.

scholarly journals ON WEYL'S THEOREM FOR TENSOR PRODUCTS

2012 ◽  
Vol 55 (1) ◽  
pp. 139-144 ◽  
Author(s):  
C. S. KUBRUSLY ◽  
B. P. DUGGAL
Keyword(s):  
Tensor Products ◽  
Weyl’S Theorem ◽  
Infinite Dimensional ◽  
Weyl Spectrum

AbstractLetAandBbe operators acting on infinite-dimensional spaces. In this paper we prove that ifAandBare isoloid, satisfy Weyl's theorem, and the Weyl spectrum identity holds, thenA⊗Bsatisfies Weyl's theorem.

Tensor products which do not preserve operator algebras

1990 ◽  
Vol 108 (2) ◽  
pp. 395-403 ◽  
Author(s):  
David P. Blecher
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Operator Algebras ◽  
Tensor Products ◽  
Preserve Operator ◽  
Infinite Dimensional ◽  
Hilbert Space Operators ◽  
Algebra Of Operators

Of late the link between operator algebras and certain tensor products has been reiterated [5]. We prove here that the projective and Haagerup tensor products of two infinite-dimensional C*-algebras is not even topologically isomorphic to an algebra of operators on a Hilbert space. Estimates are given for the distance of the tensor product from such an algebra. Nonetheless with respect to a natural multiplication the Haagerup tensor product of two algebras of Hilbert space operators is completely isometrically isomorphic to an algebra of operators on some B(ℋ).

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