Preslikave, ki približno ohranjajo ortogonalnost : doktorska disertacija
Mojškerc, Blaž
V prostorih s skalarnim produktom so linearne preslikave, ki ohranjajo ortogonalnost, natanko skalarni večkratniki izometrij. Zastavi se vprašanje, kako se da ta rezultat posplošiti. Ker v splošnih ...normiranih prostorih skalarni produkt ne obstaja, je treba najti drug način za uvedbo ortogonalnosti. Uporabimo Birkhoff-Jamesovo definicijo ortogonalnosti, in podamo njene osnovne lastnosti. V nadaljevanju pokažemo, da so tudi v splošnih normiranih prostorih linearne preslikave, ki ohranjajo Birkhoff-Jamesovo ortogonalnost, natanko skalarni večkratniki izometrij. Nato si ogledamo še drugo posplošitev, študiramo namreč linearne preslikave, ki približno ohranjajo ortogonalnost. Izkaže se, da so linearne preslikave, ki približno ohranjajo ortogonalnost v Hilbertovih prostorih, vedno "blizu" linearnim preslikavam, ki ohranjajo ortogonalnost. Za zaključek združimo obe smeri posplošitev, študiramo preslikave, ki približno ohranjajo ortogonalnost v splošnih normiranih prostorih.
Type of material - dissertation
; adult, serious
Publication and manufacture - Ljubljana : [B. Mojškerc], 2012
GS II 0000714688 glavno skladišče
GS II 714688 glavno skladišče
available - reading room
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