EUDML

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 $u$ -ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.

On a result of J. Johnson

Kamil John — 1995

Czechoslovak Mathematical Journal

$w^{*}$ -basic sequences and reflexivity of Banach spaces

Kamil John — 2005

Czechoslovak Mathematical Journal

We observe that a separable Banach space $X$ is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if $ℒ (X, Y)$ is not reflexive for reflexive $X$ and $Y$ then $ℒ (X_{1}, Y)$ is is not reflexive for some $X_{1} \subset X$ , $X_{1}$ having a basis.

Pták's characterization of reflexivity in tensor products

Kamil John — 2006

Czechoslovak Mathematical Journal

We characterize the reflexivity of the completed projective tensor products $X {\tilde{\otimes}}_{π} Y$ of Banach spaces in terms of certain approximative biorthogonal systems.

On the uncomplemented subspace $K (X, Y)$

Kamil John — 1992

Czechoslovak Mathematical Journal

Projections from $L (X, Y)$ onto $K (X, Y)$

Kamil John — 2000

Commentationes Mathematicae Universitatis Carolinae

Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let $X$ and $Y$ be Banach spaces such that $X$ is weakly compactly generated Asplund space and $X^{*}$ has the approximation property (respectively $Y$ is weakly compactly generated Asplund space and $Y^{*}$ has the approximation property). Suppose that $L (X, Y) \neq K (X, Y)$ and let $1 < λ < 2$ . Then $X$ (respectively $Y$ ) can be equivalently renormed so that any projection $P$ of $L (X, Y)$ onto $K (X, Y)$ has the sup-norm greater or equal to $λ$ .

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On Tensor Product Characterization of Nuclear Spaces.

Tensor Product of Several Spaces and Nuclearity.

Counterexample to a Conjecture of Grothendieck.

On the compact non-nuclear operator problem.

Some remarks on compact maps in Banach spaces

Compact non-nuclear operator problem

Operators whose tensor powers are $ε$ - $π$ -continuous

Zwei Charakterisierungen der nuklearen lokalkonvexen Räume

A remark on Schwartz spaces consistent with a duality

Schwartz spaces consistent with a duality

U-ideals of factorable operators

On a result of J. Johnson

$w^{*}$ -basic sequences and reflexivity of Banach spaces

Pták's characterization of reflexivity in tensor products

On the uncomplemented subspace $K (X, Y)$

Projections from $L (X, Y)$ onto $K (X, Y)$

Weak compact generating in duality

A note on strong differentiability spaces

On rough norms on Banach spaces

On the equality of injective and projective tensor products