2017/12/21 by Alan Kamuda, Kamuda, Alan, Sergiusz Kużel +1
Mathematics · #46C20 #47B50 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46C20 #msc:47B50
paper · pdf · doi:10.48550/arxiv.1712.08050
15 pages.arXiv admin note: text overlap with arXiv:1703.03665 by other authors
arxiv created 2018/01/07 · arxiv updated 2018/01/09
A definition of frames in Krein spaces is proposed which extends the concept of J-frames defined by J.I. Giribet et al., J. Math. Anal. Appl. 393 (2012), 122-137. The principal difference consists in the fact that a J-frame is related to maximal definite subspaces M_± which are not assumed to be uniformly definite. The latter allows one to extend the collection of J-frames. In particular, some complete J-orthogonal sequences and J-orthogonal Schauder bases can be interpreted as J-frames.