A Note on -Morphisms of Hilbert H-Modules
In this paper, we demonstrate notion of -morphism of Hilbert H-modules and describe some properties of these module maps. Moreover, we show that if : A ! B is an injective morphism of simple H-algebras, the range of |(A) is B-closed, {ei}i2I is a maximal family of doubly orthogonal minimal proj...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Islamic Azad University
2015-03-01
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| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/295 |
| Summary: | In this paper, we demonstrate notion of -morphism of
Hilbert H-modules and describe some properties of these module maps.
Moreover, we show that if : A ! B is an injective morphism of simple
H-algebras, the range of |(A) is B-closed, {ei}i2I is a maximal
family of doubly orthogonal minimal projections for A, : E ! F is a
surjective -morphism of Hilbert H-modules, {u,i}2 is an orthonormal
basis for E in which for each 2 , [u,i|u,i] = ei (i 2 I) and
F is full, then {(ei)}i2I and {(u,i)}2 are maximal family of doubly
orthogonal minimal projections for B and orthonormal basis for F
respectively. |
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| ISSN: | 1735-8299 1735-8299 |