On the uncomplemented subspace
Kamil John (1992)
Czechoslovak Mathematical Journal
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Displaying similar documents to “Uncomplementability of the spaces of norm continuous functions in some spaces of 'weakly' continuous functions”
On the uncomplemented subspace
Isomorphic properties of Banach spaces of continuous functions
Z. Semadeni (1963)
Studia Mathematica
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Factorization of compact operators and finite representability of Banach spaces with applications to Schwartz spaces
Steven Bellenot (1978)
Studia Mathematica
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Sobczyk's theorems from A to B.
Félix Cabello Sánchez, Jesús M. Fernández Castillo, David Yost (2000)
Extracta Mathematicae
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Sobczyk's theorem is usually stated as: . Nevertheless, our understanding is not complete until we also recall: . Now the limits of the phenomenon are set: although c is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l.
Ultraweakly compact operators and dual spaces
Teresa Alvarez (2004)
Bollettino dell'Unione Matematica Italiana
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In this paper, the class of all bounded ultraweakly compact operators in Banach spaces is introduced and characterised in terms of their first and second conjugates. We analize the relationship between an ultraweakly compact operator and its conjugate. Examples of operators belonging to this class are exhibited. We also investigate the connection between ultraweak compactness of and minimal subspaces of and we present a result of factorisation for ultraweakly compact operators. ...
Complemented and uncomplemented subspaces of Banach spaces.
Anatolij M. Plichko, David Yost (2000)
Extracta Mathematicae
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Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.
Total subspaces in dual Banach spaces which are not norming over any infinite-dimensional subspace
M. Ostrovskiĭ (1993)
Studia Mathematica
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The main result: the dual of separable Banach space X contains a total subspace which is not norming over any infinite-dimensional subspace of X if and only if X has a nonquasireflexive quotient space with a strictly singular quotient mapping.
On essentially incomparable Banach spaces.
Manuel González (1991)
Extracta Mathematicae
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We introduce the concept of essentially incomparable Banach spaces, and give some examples. Then, for two essentially incomparable Banach spaces X and Y, we prove that a complemented subspace of the product X x Y is isomorphic to the product of a complemented subspace of X and a complemented subspace of Y. If, additionally, X and Y are isomorphic to their respective hyperplanes, then the group of invertible operators in X x Y is not connected. The results can be applied to some classical...