scholarly journals A class of Banach spaces with few non-strictly singular operators

2005 ◽  
Vol 222 (2) ◽  
pp. 306-384 ◽  
Author(s):  
S.A. Argyros ◽  
J. Lopez-Abad ◽  
S. Todorcevic
Keyword(s):  
Banach Spaces ◽  
Singular Operators ◽  
Strictly Singular

scholarly journals ON STRICTLY SINGULAR OPERATORS BETWEEN SEPARABLE BANACH SPACES

Mathematika ◽  
2010 ◽  
Vol 56 (2) ◽  
pp. 285-304 ◽  
Author(s):  
Kevin Beanland ◽  
Pandelis Dodos
Keyword(s):  
Banach Spaces ◽  
Singular Operators ◽  
Strictly Singular

scholarly journals Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Abdelkader Dehici ◽  
Khaled Saoudi
Keyword(s):  
Banach Spaces ◽  
Fredholm Operators ◽  
Singular Operators ◽  
Lower Semi ◽  
Strictly Singular ◽  
Densely Defined

We show the existence of Banach spacesX,Ysuch that the set of strictly singular operators𝒮(X,Y)(resp., the set of strictly cosingular operators𝒞𝒮(X,Y))would be strictly included inℱ+(X,Y)(resp.,ℱ−(X,Y))for the nonempty class of closed densely defined upper semi-Fredholm operatorsΦ+(X,Y)(resp., for the nonempty class of closed densely defined lower semi-Fredholm operatorsΦ−(X,Y)).

scholarly journals Improjective operators and ideals in a category of Banach spaces

1972 ◽  
Vol 14 (3) ◽  
pp. 274-292 ◽  
Author(s):  
E. Tarafdar
Keyword(s):  
Banach Spaces ◽  
Compact Operator ◽  
Closed Subspace ◽  
Linear Operators ◽  
Singular Operator ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Singular Operators ◽  
Strictly Singular ◽  
Schauder Theorem

Kato [3] has introduced a class of operators called strictly singular operators. These operators have many properties in common with compact operators. In fact the concept of a strictly singular operator is an extension of the concept of a compact operator. Kato has proved that if X and X′ are Banach Spaces, then the singular operators of X into X′ forms a closed subspace of the space of bounded linear operators of X into X′ and if X = X′, then these operators forms a two-sided ideal in the ring of bounded linear operators on X. He has also shown that the Riers-Schauder theorem holds for the spectrum of a strictly singular operator. Gohberg, Feldman and Markus [23] have treated the same class of operators with an equivalent definition.

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