On some Banach ideals of operators
O. Reynov (1981)
Studia Mathematica
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O. Reynov (1981)
Studia Mathematica
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Stefan Heinrich
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CONTENTSIntroduction............................................................................... 5Notation............................................................................................. 61. Finite representability of operators.......................................... 72. Super-ideals of operators......................................................... 143. Connections with Banach space theory................................. 204. Procedures on super-ideals........................................................
Asvald Lima (1979)
Mathematica Scandinavica
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Johan Swart, Jan H. Fourie (1981)
Manuscripta mathematica
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Víctor M. Sánchez (2017)
Open Mathematics
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There are just a few general criteria on spaceability. This survey paper is the history of one of the first ones. Let I1 and I2 be arbitrary operator ideals and E and F be Banach spaces. The spaceability of the set of operators I1(E, F) I2(E, F) is studied. Before stating the criterium, the paper summarizes the main results about lineability and spaceability of differences between particular operator ideals obtained in recent years. They are the seed of the ideas contained in the general...
Ehrhard Behrends (1988)
Studia Mathematica
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Yoshiaki Okazaki, Yashuii. Takahashi (1988)
Mathematische Annalen
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Carsten Michels (2007)
Studia Mathematica
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As a continuation of the work of Bennett and Carl for the case q = ∞, we consider absolutely (r,p,q)-summing inclusion maps between Minkowski sequence spaces, 1 ≤ p,q ≤ 2. Using these results we deduce parts of the limit orders of the corresponding operator ideals and an inclusion theorem between the ideals of (u,s,t)-nuclear and of absolutely (r,p,q)-summing operators, which gives a new proof of a result of Carl on Schatten class operators. Furthermore, we also consider inclusions between...
Manuel González, Antonio Martinón (1990)
Extracta Mathematicae
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Klaus Saatkamp (1978)
Mathematische Zeitschrift
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Kamil John (1999)
Czechoslovak Mathematical Journal
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We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons’s construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are -ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.
G. Bennett (1976)
Studia Mathematica
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