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Operators in vector sequence spaces. (Spanish: Operadores en espacios de sucesiones vectoriales)

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Bombal Gordón, Fernando (1988) Operators in vector sequence spaces. (Spanish: Operadores en espacios de sucesiones vectoriales). Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid, 82 (1). pp. 157-160. ISSN 0034-0596

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Official URL: http://www.rac.es/ficheros/Revistas/REV_20091030_00646.pdf


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Abstract

For an arbitrary sequence of Banach spaces, the space of corresponding vector-valued, p  -summable sequences is considered, 1≤p<∞  . Each bounded linear operator from such a space into an arbitrary Banach space is identified by the corresponding coordinate sequence, that is, by the sequence of its restrictions to each summand. Simple criteria for an operator to be compact, weakly compact, Dieudonné, Dunford-Pettis and unconditionally convergent are given in terms of its coordinate sequence. Corresponding Banach space properties defined by the operator ideals mentioned above are reduced to the same properties for each summand.


Item Type:Article
Uncontrolled Keywords:Banach spaces;
Subjects:Sciences > Mathematics > Topology
ID Code:18156
Deposited On:04 Feb 2013 09:44
Last Modified:07 Feb 2014 10:00

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