International Journal of Modern Mathematical Sciences
ISSN: 2166-286X (online)Search Article(s) by:
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Current Issue: Vol. 11 No. 3or Keyword in Title:
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Table of Content for Vol. 11 No. 3, 2014

Distribution of Spectrum in a Direct Sum Decomposition of Operators into Normal and Completely Non-Normal Parts
Mwenda E., Musundi S. W., Nzimbi B. M., Marani V. N. and Loyford N.
      
 PP. 118 - 124
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ABSTRACT: We discuss the distribution of spectra of a direct sum decomposition of an arbitrary operator into normal and completely non normal parts. We utilize the fact that any given operator T∈B(H) can be decomposed into a direct summand T=T1⊕T2 with T1 and T2 are the normal and completely non normal parts respectively. This canonical decomposition is preferred to other forms of decomposition such as Polar and Cartesian decompositions because these two do not transfer certain properties (for instance the spectra, numerical range, and numerical radius) from the original /decomposed operator to the constituent parts. This is presumably done since these parts are simpler to deal with.


New Type of Sequence Space and Matrix Transformations
Ab. Hamid Ganie, Neyaz Ahmad Sheikh, Tanweer Jalal
      
 PP. 125 - 129
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ABSTRACT: The main purpose of the present paper is to determine the necessary and sufficient conditions on a matrix sequence A=(Av) in order that A belongs to the matrix class (bv(u,p):C) where 0<p<=∞.