The precompactness–lemma
The projective tensor product of Fréchet-Montel spaces
The space of all bounded operators on Hilbert space does not have the approximation property
The space of compact operators contains when a noncompact operator is suitably factorized
The symmetric tensor product of a direct sum of locally convex spaces
An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to its square .
Topological tensor products and asymptotic developments
Topological tensor products of a Fréchet-Schwartz space and a Banach space
We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that is not an inductive limit of normed spaces for some Banach space X. This solves in the negative open questions of Bierstedt, Meise and Hollstein. As a consequence we obtain Fréchet-Schwartz spaces F and Banach spaces X such that the problem of topologies of Grothendieck has a negative answer for . This solves in the negative a question of Taskinen. We also give...
Triangularization of some families of operators on locally convex spaces
Some results concerning triangularization of some operators on locally convex spaces are established.
U-ideals of factorable operators
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.
Ultra-b-barrelled spaces and the completeness of
Uncomplementability of spaces of compact operators in larger spaces of operators
In the first part of the paper we prove some new result improving all those already known about the equivalence of the nonexistence of a projection (of any norm) onto the space of compact operators and the containment of in the same space of compact operators. Then we show several results implying that the space of compact operators is uncomplemented by norm one projections in larger spaces of operators. The paper ends with a list of questions naturally rising from old results and the results...
Weak Compactness of Multiplication Operators on Spaces of Bounded Linear Operators.
Weak Grothendieck's theorem.
Weak-norm sequentially continuous operators
Weakly compact wedge operators on Köthe echelon spaces.
Zur Lototsky - Transformation über kompakten Räumen von Wahrscheinlichkeitsmassen.
Внутренние характеризации некоторых классов опорных множеств
Двусторонние замкнутые идеалы алгебры линейных операторов в некоторых пространствах последовательностей
Замечания о векторной двойственности.
Отсутствие локально безусловной структуры в некоторых пространствах операторов