


Paper's Title:
BirkhoffJames orthogonality and Best Approximant in L_{1}(X)
Author(s):
Mecheri Hacene and Rebiai Belgacem
Department of Mathematics and
Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
Email: mecherih2000@yahoo.fr
Department of Mathematics and
Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
Email: brebiai@gmail.com
Abstract:
Let X be a complex Banach space and let (X,ρ) be a positive measure space. The BirkhoffJames orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We use this notion of orthogonality to establish a new characterization of BirkhoffJames orthogonality of bounded linear operators in L_{1}(X,ρ) also implies best approximation has been proved.
Paper's Title:
Weyl's theorem for class Q and k  quasi class Q Operators
Author(s):
S. Parvatham and D. Senthilkumar
Department of Mathematics and Humanities,
Sri Ramakrishna Institute of Technology, Coimbatore10, Tamilnadu,
India.
Email: parvathasathish@gmail.com
Post Graduate and Research Department of
Mathematics,
Govt. Arts College, Coimbatore641018, Tamilnadu,
India.
Email: senthilsenkumhari@gmail.com
Abstract:
In this paper, we give some properties of class Q operators. It is proved that every class Q operators satisfies Weyl's theorem under the condition that T^{2} is isometry. Also we proved that every k quasi class Q operators is Polaroid and the spectral mapping theorem holds for this class of operator. It will be proved that single valued extension property, Weyl and generalized Weyl's theorem holds for every k quasi class Q operators.
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