Search the digital library catalog

Abstract: Glavni rezultat članka karakterizira zvezne bilinearne preslikave ▫$phi$▫ iz ▫$C^1[0,1] times C^1[0,1]$▫ v Banachov prostor ▫$X$▫ z lastnostjo, da iz ▫$fg=0$▫ sledi ▫$phi(f,g) = 0$▫. Ta rezultat se uporabi pri študiju ohranjevalcev ničelnega produkta na ▫$C^1[0,1]$▫ in pri študiju operatorjev na ▫$C^1[0,1]$▫, ki zadoščajo neki verzijo pogoja o lokalnosti operatorja.
Keywords: matematika, teorija operatorjev, zvezne odvedljive funkcije, bilinearni ohranjevalci ničelnega produkta, linearni ohranjevalci ničelnega produkta, lokalni operator, mathematics, operator theory, continuously differentiable functions, zero product preserving bilinear map, zero product preserving linear map, local operator
Published in DKUM: 10.07.2015; Views: 1192; Downloads: 48
Link to full text

Abstract: Let ▫$H$▫ be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of ▫$mathscr{B}(H)$▫, the algebra of all bounded linear operators on a Hilbert space ▫$H$▫, is an automorphism.
Keywords: mathematics, operator theory, automorphism, local automorphism, algebra of operators on a Hilbert space
Published in DKUM: 07.06.2012; Views: 1533; Downloads: 94
Link to full text