The Partial Inner Product Space Method: A Quick Overview

The Partial Inner Product Space Method: A Quick Overview

Many families of function spaces play a central role in analysis, in particular, in signal processing e.g., wavelet or Gabor analysis . Typical are L spaces, Besov spaces, amalgam spaces, or modulation spaces. In all these cases, the parameter indexing the family measures the behavior regularity, decay properties of particular functions or operators. It turns out that all these space families a...

Partial Inner Product Spaces: Some Categorical Aspects

The Lanczos Method with Semi-inner Product

The spectral transformation Lanczos method is very popular for solving large scale Her-mitian generalized eigenvalue problems. The method uses a special inner product so that the symmetric Lanczos method can be used. Sometimes, a semi-inner product must be used. This may lead to instabilities and breakdown. In this paper, we suggest a cure for breakdown by use of an implicit restart in the Lanc...

$C^{*}$-semi-inner product spaces

In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.

A Comparative Study of Fuzzy Inner Product Spaces

In the present paper, we investigate a connection between two fuzzy inner product one of which arises from Felbin's fuzzy norm and the other is based on Bag and Samanta's fuzzy norm. Also we show that, considering a fuzzy inner product space, how one can construct another kind of fuzzy inner product on this space.