Extending certain transformation group actions in separable, infinite-dimensional Frechet spaces and the Hilbert cube
نویسندگان
چکیده
منابع مشابه
Extending Certain Transformation Group Actions in Separable, Infinite-dimensional Frechet Spaces and the Hilbert Cube
A theorem of V. L. Klee, Jr. [9] asserts that any homeomorphism between two compact sets in a separable, infinite-dimensional Hilbert space can be extended to a homeomorphism of the entire space onto itself. Since it has recently been shown ( [ l ] , [5] and [6]) that all separable, infinite-dimensional Frechet spaces are homeomorphic (a Frechet space being a metrizable, complete, locally conve...
متن کاملPhase Retrieval in Infinite-dimensional Hilbert Spaces
The main result of this paper states that phase retrieval in infinitedimensional Hilbert spaces is never uniformly stable, in sharp contrast to the finite-dimensional setting in which phase retrieval is always stable. This leads us to derive stability results for signals depending on how well they are approximated by finite expansions.
متن کاملPseudo-Hermiticity in infinite-dimensional Hilbert spaces
In infinite-dimensional Hilbert spaces, the application of the concept of pseudo-Hermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to difficulties related to the definition of the metric operator. These difficulties are illustrated by examining some examples taken from the recent literature. We present a formulation that avoids such problems. PACS numbers: ...
متن کاملQuasi-Hermiticity in infinite-dimensional Hilbert spaces
In infinite-dimensional Hilbert spaces, the application of the concept of quasiHermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to problems related to the definition of the metric operator. We discuss these problems by examining some examples taken from the recent literature and propose a formulation that is free of these difficulties.
متن کاملOptimization in infinite-dimensional Hilbert spaces
We consider the minimization of convex functionals on a real Hilbert space. The requisite theory is reviewed, and concise proofs of the relevant results are given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1968
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1968-12119-6