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Topological degree theory in fuzzy metric spaces

M.H.M. Rashid (2019)

Archivum Mathematicum

The aim of this paper is to modify the theory to fuzzy metric spaces, a natural extension of probabilistic ones. More precisely, the modification concerns fuzzily normed linear spaces, and, after defining a fuzzy concept of completeness, fuzzy Banach spaces. After discussing some properties of mappings with compact images, we define the (Leray-Schauder) degree by a sort of colimit extension of (already assumed) finite dimensional ones. Then, several properties of thus defined concept are proved....

Topological dual of B ∞ ( I , ₁ ( X , Y ) ) with application to stochastic systems on Hilbert space

N.U. Ahmed (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural...

Topological entropy and differential equations

Ján Andres, Pavel Ludvík (2023)

Archivum Mathematicum

On the background of a brief survey panorama of results on the topic in the title, one new theorem is presented concerning a positive topological entropy (i.e. topological chaos) for the impulsive differential equations on the Cartesian product of compact intervals, which is positively invariant under the composition of the associated Poincaré translation operator with a multivalued upper semicontinuous impulsive mapping.

Topologies and bornologies determined by operator ideals, II

Ngai-Ching Wong (1994)

Studia Mathematica

Let be an operator ideal on LCS’s. A continuous seminorm p of a LCS X is said to be - continuous if Q ̃ p ∈ i n j ( X , X ̃ p ) , where X ̃ p is the completion of the normed space X p = X / p - 1 ( 0 ) and Q ̃ p is the canonical map. p is said to be a Groth()- seminorm if there is a continuous seminorm q of X such that p ≤ q and the canonical map Q ̃ p q : X ̃ q → X ̃ p belongs to ( X ̃ q , X ̃ p ) . It is well known that when is the ideal of absolutely summing (resp. precompact, weakly compact) operators, a LCS X is a nuclear (resp. Schwartz, infra-Schwartz) space if and only if every continuous...

Topologies on the group of invertible transformations

Maciej Burnecki, Robert Rałowski (2011)

Banach Center Publications

We enlarge the amount of embeddings of the group G of invertible transformations of [0,1] into spaces of bounded linear operators on Orlicz spaces. We show the equality of the inherited coarse topologies.

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