A Note on Phi-Morphisms of Hilbert H*-Modules

Authors

  • Mahnaz Khanehgir Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran, Mashhad 91735, Iran.
  • Marzeh Moradian Kheibari Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran, Mashhad 91735, Iran.

DOI:

https://doi.org/10.30495/jme.v9i0.295

Keywords:

full Hilbert H*-module, -morphism, minimal projection, unitary operator..

Abstract

In this paper, we demonstrate notion of -morphism of Hilbert H-modulesand describe some properties of these module maps. Moreover, we show that if : A ! Bis an injective morphism of simple H-algebras, the range of j(A) is B-closed, feigi2I is amaximal family of doubly orthogonal minimal projections for A, : E ! F is a surjective-morphism of Hilbert H-modules, fu;ig2 is an orthonormal basis with supportingprojection ei (i 2 I) for E and F is full, then f(ei)gi2I and f(u;i)g2 are maximal familyof doubly orthogonal minimal projections for B and orthonormal basis for F respectively.

Author Biographies

Mahnaz Khanehgir, Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran, Mashhad 91735, Iran.

Islamic Azad University.Mashhad Branch

Marzeh Moradian Kheibari, Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran, Mashhad 91735, Iran.

Islamic Azad University.Mashhad Branch

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Published

2015-05-17

Issue

Vol. 9

Section

Vol. 9, No. 1, (2015)

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