Rigid subsets in Euclidean and Hilbert spaces

Analytic Subsets of Hilbert Spaces †

We show that every complete metric space is homeomorphic to the locus of zeros of an entire analytic map from a complex Hilbert space to a complex Banach space. As a corollary, every separable complete metric space is homeomorphic to the locus of zeros of an entire analytic map between two complex Hilbert spaces. §1. Douady had observed [8] that every compact metric space is homeomorphic to the...

Volume Distortion for Subsets of Euclidean Spaces

In [Rao, SoCG 1999], it is shown that every n-point Euclidean metric with polynomial spread admits a Euclidean embedding with k-dimensional distortion bounded by O( √ log n log k), a result which is tight for constant values of k. We show that this holds without any assumption on the spread, and give an improved bound of O( √ log n(log k)). Our main result is an upper bound of O( √ log n log lo...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Generalized Frames in Hilbert Spaces

FUSION FRAMES IN HILBERT SPACES

Fusion frames are an extension to frames that provide a framework for applications and providing efficient and robust information processing algorithms. In this article we study the erasure of subspaces of a fusion frame.