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EP modular operators and their products

Kamran Sharifi

Abstract

We study first EP modular operators on Hilbert C*-modules and then we provide necessary and sufficient conditions for the product of two EP modular operators to be EP. These enable us to extend some results of Koliha [{\it Studia Math.} {\bf 139} (2000), 81--90.] for an arbitrary C*-algebra and the C*-algebras of compact operators.

EP modular operators and their products

Abstract

We study first EP modular operators on Hilbert C*-modules and then we provide necessary and sufficient conditions for the product of two EP modular operators to be EP. These enable us to extend some results of Koliha [{\it Studia Math.} {\bf 139} (2000), 81--90.] for an arbitrary C*-algebra and the C*-algebras of compact operators.

Paper Structure

This paper contains 3 sections, 10 theorems, 22 equations.

Table of Contents

  1. Introduction.
  2. Preliminaries
  3. On the product of ep modular operators

Key Result

Proposition 2.2

Let $X$ be a Hilbert $\mathcal{A}$-module and $T \in \mathcal{L}(X)$ have a closed range. Then the following conditions are equivalent:

Theorems & Definitions (19)

  • Definition 2.1
  • Proposition 2.2
  • proof
  • Lemma 3.1
  • proof
  • Proposition 3.2
  • proof
  • Proposition 3.3
  • proof
  • Example 3.4
  • ...and 9 more