Ordered Structures of Constructing Operators for Generalized Riesz Systems

Hiroshi Inoue

International Journal of Mathematics and Mathematical Sciences, 2018, vol. 2018, 1-8

Abstract:

A sequence in a Hilbert space with inner product is called a generalized Riesz system if there exist an ONB in and a densely defined closed operator in with densely defined inverse such that and , , and is called a constructing pair for and is called a constructing operator for . The main purpose of this paper is to investigate under what conditions the ordered set of all constructing operators for a generalized Riesz system has maximal elements, minimal elements, the largest element, and the smallest element in order to find constructing operators fitting to each of the physical applications.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:3268251

DOI: 10.1155/2018/3268251

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