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Título:
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The weak summability dominion of a sequence S of the Hilbert space in relation with the set of linear bounded operators
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Autores:
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Martín Peinador, Elena
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Tipo de documento:
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texto impreso
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Editorial:
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Universidad Nacional Autónoma de México, 1981
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/restrictedAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Topología
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Tipo = Artículo
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Resumen:
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Let H be a separable, real Hilbert space, L(H) the Banach space of all bounded linear operators on H. For a given sequence (xn)n?N?H with xn?0 for all n?N let C(xn):={T?L(H):?n?NTxn} and M(xn):={x?H:? n?N|(xn,x)|}. The author studies injective (i.e. one-to-one, not necessarily invertible) operators, finite rank operators, and completely continuous operators in C(xn). The following results are shown: (1) C(xn) contains an injective operator if and only if M (xn)=H. (2) C(xn) is contained in the set of all finite rank operators on H if and only if the linear subspace M (xn)?H is of finite dimension. (3) C(xn) contains operators which are not completely continuous if and only if M(xn) contains an infinite-dimensional closed linear subspace of H. Finally it is proved that whenever all operators in C(xn) are completely continuous, they must necessarily be Hilbert-Schmidt operators.
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En línea:
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https://eprints.ucm.es/id/eprint/21933/1/MPeinador113.pdf
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