IJPAM: Volume 106, No. 4 (2016)

UNIVERSALITY AND TRANSITIVITY OF
SEMIGROUPS OF OPERATORS

A. Tajmouati$^1$, M. Amouch$^2$, M.R.F. Alhomidi Zakariya$^3$, M. Abkari$^4$
$^{1,3,4}$Faculty of Sciences
Sidi Mohamed Ben Abdellah Univeristy
Dhar Al Mahraz Fez, MOROCCO
$^2$Department of Mathematics
University Chouaib Doukkali
Faculty of Sciences
Eljadida, 24000, Eljadida, MOROCCO


Abstract. Let $B(X)$ denote the algebra of all bounded linear operators on a infinite-dimensional separable complex Banach space $X$ and $M$ a nonzero subspace of $X.$ In this paper we study the notion of disjoint or diagonally subspace universal respect to $M$ ( in short $d-M$ universal) and the notion of d-M topologically transitive for the sequence

\begin{displaymath}(T_{1,t})_{ t\geq0},(T_{2,t})_{t\geq0},...,(T_{N,t})_{t\geq0},(N\geq 2)\end{displaymath}

of a $C0$-semigroups of operators on $X.$ Also, we give a necessary and sufficient condition for which this sequence is be d-M topologically transitive.

Received: October 28, 2015

AMS Subject Classification: 47A16, 47D06, 47D03

Key Words and Phrases: Banach space operators, $C_0$ semigroups, diagonally subspace universal, topologically transitive

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DOI: 10.12732/ijpam.v106i4.10 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 4
Pages: 1087 - 1094


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