Progress in Functional Analysis, Proceedings of the by Klaus D. Bierstedt, José Bonet, John Horváth and Manuel

By Klaus D. Bierstedt, José Bonet, John Horváth and Manuel Maestre (Eds.)

This quantity contains a choice of study articles in practical research, celebrating the party of Manuel Valdivia's 60th birthday. The papers integrated within the quantity are in line with the most lectures provided in the course of the overseas sensible research assembly held in Pe#iscola (Valencia, Spain) in October 1990. in the course of his profession, Valdivia has made contributions to a large choice of components of sensible research and his paintings has had a profound impression. an intensive appreciation of Valdivia's paintings is gifted in J. Horvath's article. In honor of Valdivia's achievements, this quantity offers greater than twenty-five papers on subject matters with regards to his study (Banach areas, operator beliefs, tensor items, Frechet, (DF) and (LF) areas, distribution idea, countless holomorphy etc.). whereas nearly all of papers are learn articles, survey articles also are integrated. The booklet covers a vast spectrum of pursuits in modern-day sensible research and provides new effects by means of prime experts within the box.

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SEQUENCES AND FAMILIES OF CONTINUOUS, INTEGRABLE AND HOLOMORPHIC FUNCTIONS Valdivia's research career did, however, not start with the explosion of 1968. In his doctoral dissertation [ I ] he considers concepts which are usually defined for maps from a topological space into a metric space or a uniform space. He characterizes uniformly convergent, equicontinuous, Cauchy, and quasi-uniformly convergent sequences of maps from a metric space X into a metric space Y, and then uses the characterizations to define these concepts when X let and be a topological space, Y X Y a regular topological space, and (f,) a sequence of continuous maps from X a map f : X+Y.

U,x> = 1 for all Let G There exists u E E' such XEG. 5. CLOSED GRAPH AND OPEN MAPPING THEOREMS It is remarkable that barrelled spaces, originally introduced to generalize the uniform boundedness principle, also play a role in closed graph theorems. M. (1)). e. for every neighborhood W of -1 the closure of u (W) is a neighborhood of 0 in E (19, 934, a space F 0 in F 6 . 1 V. (8)). , such that G is the dual of F equipped f with 7 . 8). e. coincides with E'. Analogously E is a f Ptak space (or B-complete) if every 7 -closed subspace of E' is o(E1,E)closed {19,§34,2).

ZOl)), then the Schwartz). F are reflexive (resp. Montel, n The mathematical works of Manuel Valdivia Baire-hyperplane spaces [68] are those in which every union of a sequence of closed hyperplanes has a void interior. Every metrizable (ZY)space is a Baire-hyperplane space. Let E be either an infinite- dimensional, separable Frechet space or a locally complete inductive limit of infinite-dimensional, separable Frechet spaces. A construction similar to one given in [771 shows that there exist two dense subspaces F of and G E such that G is ultrabornological and a hyperplane in F, and F is barrelled and not the inductive limit of Baire-hyperplane spaces.

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