Direct Images, Fields of Hilbert Spaces, and Geometric Quantization

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...

Ultra Bessel sequences in direct sums of Hilbert spaces

In this paper, we establish some new results in ultra Bessel sequences and ultra Bessel sequences of subspaces. Also, we investigate ultra Bessel sequences in direct sums of Hilbert spaces. <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-s...

The Geometric Tools of Hilbert Spaces

Supersymmetric Distributions, Hilbert Spaces of Supersymmetric Functions and Quantum Fields

The recently investigated Hilbert-Krein and other positivity structures of the superspace are considered in the framework of superdistributions. These tools are applied to problems raised by the rigorous supersymmetric quantum field theory.

Non Asymptotic Bounds for Vector Quantization in Hilbert Spaces

Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of O(1/n), where n is the sample size (see, e.g., [9] or [17]). This rate is attained for the empirical risk minimizer strategy, if the source distribution satis es some regularity conditions. However, the dependency of the average distortion on other parameters is not known, and...