"Anal\u00FDza v Banachov\u00FDch prostorech"@cs . "Analysis in Banach Spaces"@en . "2005-01-01+01:00"^^ . . "The aim of the project is to study further some open problems in geometrical anaysis in Banach spaces. Some of these problems were already studied in the diploma and Ph.D. thesis of the applicant. These questions are studied also at the department of functional analysis of the Mathematical institute of the Czech academy of sciences, with which the applicant wants to collaborate clo sely. We expect to study the problems in the renorming theory of Banach spaces as well as the questions concerning the smoothness, in particular smoothness of the higher order. It involves studying the impact of the existence of various kind of rotund or smooth norms (or other structures) on the overall structure of the space. An important part of these problems in nonseparable spaces are questions related to general topology. The project will focus e.g. on the following goals: (1) completely clarify the situation in renorming characterization of the reflexive spaces; (2) a study of the functions on Orlicz spaces"@en . "393"^^ . . . "0"^^ . "393"^^ . . "geometry of Banach spaces; functional analysis"@en . "C\u00EDlem projektu je d\u00E1le se v\u011Bnovat otev\u0159en\u00FDm probl\u00E9m\u016Fm v geometrick\u00E9 anal\u00FDze na Banachov\u00FDch prostorech. N\u011Bkter\u00FDm t\u011Bmto probl\u00E9m\u016Fm se v\u011Bnoval navrhovatel ji\u017E ve sv\u00E9 diplomov\u00E9 a dizerta\u010Dn\u00ED pr\u00E1ci. T\u00E9to oblasti je v\u011Bnov\u00E1na t\u00E9\u017E pozornost na odd\u011Blen\u00ED funkcion\u00E1ln\u00ED anal\u00FDzy Matematick\u00E9ho \u00FAstavu Akademie v\u011Bd \u010CR, se kter\u00FDm hodl\u00E1 navrhovatel \u00FAzce spolupracovat. V r\u00E1mci projektu p\u0159edpokl\u00E1d\u00E1me studium probl\u00E9m\u016F z oblasti teorie renormac\u00ED, ale i probl\u00E9m\u016F t\u00FDkaj\u00EDc\u00EDch se hladkosti, p\u0159edev\u0161\u00EDm pak hladkosti vy\u0161\u0161\u00EDch\u0159\u00E1d\u016F. Jedn\u00E1 se zejm\u00E9na o vliv existence r\u016Fzn\u011B hladk\u00FDch nebo konvexn\u00EDch norem (p\u0159\u00EDpadn\u011B jin\u00FDch struktur) na obecnou strukturu prostoru. D\u016Fle\u017Eitou sou\u010D\u00E1st\u00ED t\u011Bchto probl\u00E9m\u016F v neseparabiln\u00EDch prostorech jsou ot\u00E1zky spojen\u00E9 s obecnou topologi\u00ED. Projekt hodl\u00E1 zkoumat nap\u0159\u00EDklad tyto probl\u00E9my: (1) do\u0159e\u0161en\u00ED situace okolo renorma\u010Dn\u00ED charakterizace reflexivn\u00EDch prostor\u016F; (2) studium funkc\u00ED lok\u00E1ln\u011B z\u00E1visl\u00FDch na kone\u010Dn\u011B mnoha sou\u0159adnic\u00EDch na Orliczov\u00FDch prostorech; (3) konvexifikace separuj\u00EDc\u00EDch polynom\u016F; (4)"@cs . . "0"^^ . "1"^^ . . "6"^^ . . . "2007-12-31+01:00"^^ . "6"^^ . . .