Advance in Topology and Functional Analysis — In Honour of María Jesús Chasco’s 65th Birthday

• Format: eBook
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2024
• Subjects: (locally) compact abelian group; 0-dimensional; absolutely summable sequence; aggregation function; analyticity; Applied mathematics; barrelled space; bounded set; Brunn–Minkowski inequality; character; cocycle; compact group; compactly generated space; compatible group topology; completion; convergence; determining subgroup; direct sum; distinguished space; dual bundle; duality; exotic torus; factorization; factorizations of a group; Fréchet space; Fubini’s theorem; full free subgroup; functorial subgroup; G-space; group; group action; Hamiltonian vector field; homomorphism; hypocontinuity; infinite-dimensional Lie group; injective and projective tensor product; isoperimetric inequality; k-space; Krein’s Theorem; LCA group; LCA groups; Lie algebra; Lie group; locally quasi-convex; locally quasi-convex group; Mackey group; Mathematics; Mathematics and Science; minimal group; monoid; multilinear map; n/a; normed space; nuclear group; nuclear space; permutation; Poisson bracket; Poisson vector space; Pontryagin duality; Pontryagin reflexive group; precompact; pro-Lie group; quasi-convex compactness property; quasi-convex subset; quasi-torsion element; Roelcke uniformity; Schur property; Schwartz group; semigroup; series; smoothness; strictly monotone function; sum range; summable sequence; T-subgroup; Tannaka duality; tensor product; thin subset of a group; topological group; topology; totally disconnected; totally minimal group; vector bundle; vector-valued continuous function; volumes of section of balls
• ISBN: 9783725813902; 3725813906; 3725813892; 9783725813896
• DOI: 10.3390/books978-3-7258-1390-2

The interaction between topology and functional analysis has been a wellspring of powerful mathematical ideas and developments since the early stages of both disciplines. It is obvious that many classical theorems from functional analysis have a strong topological flavour. In the other direction, probably the best-known example is the way abstract harmonic analysis informs many essential features of locally compact groups and Pontryagin duality. This influence is also exerted through many tools and concepts from the theory of topological vector spaces that have been either generalized to topological abelian groups or adopted as templates to study their structure and duality properties beyond the locally compact case. Besides topological groups, this Special Issue also contains papers on fuzzy groups, semigroups, topological vector spaces and real analysis. Their authors are well-known specialists and the different viewpoints provided by them will surely inspire future research on these exciting topics. This Special Issue pays tribute to María Jesús Chasco's mathematical career on the occasion of her 65th birthday.