. "0"^^ . . "Smoothness and geometry of Banach spaces"@en . . " scatered compact" . " C1-smoothness" . "http://www.isvav.cz/projectDetail.do?rowId=IAA1019003"^^ . "We will study the interplay between smoothness, weak topology, and biorthogonal systems in nonseparable Banach spaces. We will focus on uniformly Gateaux differentiable norms in connection with questions on the weak star separability of dual spaces and Eberlein compacta and on Gateaux differentiable norms in connections with countable tightness of dual balls. We will try to use the tool of biorthogonal systems to extend some recent results on spaces of continuous functions on trees to more general spaces. Some questions on smoothness in the classical Banach spaces will be studied, such as partitions of unity formed by uniformly Gateaux differentiable norms etc. Special attention will be given to questions on approximation by smooht norms in nonseparable spaces."@en . " uniform Eberlein compact" . . "IAA1019003" . "dependence on countably many coordinates;uniform gateaux smoothness; uniform Eberlein compact; scatered compact; uniform rotundity in every direction; pointwise semicontinuity; C1-smoothness; Cnekone\u010Dno-smoothness"@en . . "Hladkost a geometrie Banachov\u00FDch prostor\u016F" . "1"^^ . . . "Hodl\u00E1me studovat vz\u00E1jemn\u00E9 souvislosti mezi hladkost\u00ED, slabou topologi\u00ED a biortogon\u00E1ln\u00EDmi syst\u00E9my v neseparabiln\u00EDch Banachov\u00FDch prostorech. Chceme se soust\u0159edit na uniformn\u011B gateauxovsky diferencovateln\u00E9 normy v souvislosti s ot\u00E1zkami ohledn\u011B slab\u00E9 hv\u011Bzdi\u010Dkov\u00E9 separability du\u00E1ln\u00EDch prostor\u016F a uniformn\u00EDch Eberleinov\u00FDch kompakt\u016F; d\u00E1le pak na gateauxovskou hladkost norem v souvislosti se spo\u010Detnou t\u011Bsnost\u00ED du\u00E1ln\u00EDch koul\u00ED. Pokus\u00EDme se u\u017E\u00EDt ortogon\u00E1ln\u00EDch syst\u00E9m\u016F k roz\u0161\u00ED\u0159en\u00ED n\u011Bkter\u00FDch ned\u00E1vn\u00FDch v\u00FDsledk\u016F o prostorech spojit\u00FDch funkc\u00ED na stromech na obecn\u011Bj\u0161\u00ED Banachovy prostory. Budeme studovat n\u011Bkter\u00E9 ot\u00E1zky hladkosti na klasick\u00FDch Banachov\u00FDch prostorech, jako nap\u0159\u00EDklad rozklady jedni\u010Dky pomoc\u00ED uniformn\u011B gateauxovsky hladk\u00FDch norem a podobn\u011B. Zvl\u00E1\u0161tn\u00ED pozornost chceme v\u011Bnovat aproximac\u00EDm pomoc\u00ED hladk\u00FDch norem v neseparabiln\u00EDch prostorech." . . "0"^^ . "dependence on countably many coordinates" . . "Uniformn\u011B gateauxovsky hladk\u00FD prostor je Hilbertovsky generov\u00E1n, podprostor WCG prostoru charakterizov\u00E1n p\u0159es spo\u010Detn\u00E9 rozbit\u00ED jednotkov\u00E9 koule na epsilon-slab\u011B kompaktn\u00ED mno\u017Einy, analytick\u00E9 mno\u017Einy v separabiln\u00EDm du\u00E1lu dan\u00E9 derivacemi hladk\u00E9ho bumpu."@cs . . . "uniform gateaux smoothness" . . . "2004-10-27+02:00"^^ . . . " uniform rotundity in every direction" . "15"^^ . "15"^^ . . " pointwise semicontinuity" .