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: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Islamic Azad University
2015-03-01
|
| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/295 |
| id |
doaj-e92da3e91c524170a545fd948e632bb2 |
|---|---|
| record_format |
Article |
| spelling |
doaj-e92da3e91c524170a545fd948e632bb22020-11-25T03:58:33ZengIslamic Azad UniversityJournal of Mathematical Extension1735-82991735-82992015-03-01912336A Note on -Morphisms of Hilbert H-ModulesM. Khanehgir∗0M. Moradian Khibary1Mashhad Branch, Islamic Azad UniversityMashhad Branch, Islamic Azad UniversityIn 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.http://ijmex.com/index.php/ijmex/article/view/295 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. Khanehgir∗ M. Moradian Khibary |
| spellingShingle |
M. Khanehgir∗ M. Moradian Khibary A Note on -Morphisms of Hilbert H-Modules Journal of Mathematical Extension |
| author_facet |
M. Khanehgir∗ M. Moradian Khibary |
| author_sort |
M. Khanehgir∗ |
| title |
A Note on -Morphisms of Hilbert H-Modules |
| title_short |
A Note on -Morphisms of Hilbert H-Modules |
| title_full |
A Note on -Morphisms of Hilbert H-Modules |
| title_fullStr |
A Note on -Morphisms of Hilbert H-Modules |
| title_full_unstemmed |
A Note on -Morphisms of Hilbert H-Modules |
| title_sort |
note on -morphisms of hilbert h-modules |
| publisher |
Islamic Azad University |
| series |
Journal of Mathematical Extension |
| issn |
1735-8299 1735-8299 |
| publishDate |
2015-03-01 |
| description |
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. |
| url |
http://ijmex.com/index.php/ijmex/article/view/295 |
| work_keys_str_mv |
AT mkhanehgir anoteonmorphismsofhilberthmodules AT mmoradiankhibary anoteonmorphismsofhilberthmodules AT mkhanehgir noteonmorphismsofhilberthmodules AT mmoradiankhibary noteonmorphismsofhilberthmodules |
| _version_ |
1724456553821503488 |