دانلود کتاب سفر نامحدود در تئوری اپراتور – سفرهای هندسی و طیفی در فضاهای کرین

The idea of writing a monograph on operator theory on indefinite inner product spaces occurred to me about twenty years ago, after teaching a graduate course on the spectral theory of definitisable operators at the Faculty of Mathematics and Informatics of the University of Bucharest. With a lot of enthusiasm I wrote the core of the chapters on spectral theory and invited Heinz Langer to join me in this enterprise. At the beginning, Heinz showed his interest and encouraged me by performing a careful reading of those notes and providing very pertinent observations, but in the end he declined my invitation. That left me alone in this enterprise and offered me more freedom in choosing the subjects to be included, but this path proved to be dangerous in the end, as I explain below. After performing research on the geometry of Kre˘ın spaces and the spectral theory of selfadjoint definitisable operators in the 1980s as part of my PhD programme, I became more focused on studying dilation theory of operators on Kre˘ın spaces and started to work together with my friend and collaborator Tiberiu Constantinescu. Dilation theory is a heterogeneous domain full of concepts and results that may look connected in some way but not explicitly, and because of that it became clear, at least to us, that it needs some unification. Considering dilation theory from a rather general perspective, we soon realised that one way to unify most of dilation theory is to consider Hermitian kernels and their linearisations, or Kolmogorov decompositions, which turn out to be yet another face of reproducing kernel Kre˘ın spaces. Moreover, using some older ideas from mathematical physics, we also understood that some invariance under group, or ∗-semigroup, actions would open rather large avenues and connections with problems of a wider interest.