\(p\) dissipative operator
type: Item
instance of: scholarly article
title: \(p\) dissipative operator
zbMATH Open document ID: 0940.47028
author: Lixin Tian
author: Zengrong Liu
published in: Communications in Mathematical Physics
publication date: 2000-07-24T00:00:00Z
review text: The authors prove that the generalized positive \(p\)-selfadjoint operators in Banach space satisfy the generalized Schwartz inequality and solve the maximal dissipative extension representation of \(p\)-dissipative operators in Banach space. The paper starts with the introduction of generalized Schwartz inequality of generalized positive selfadjoint operators in generalized semi-inner product space. Next, the generalized indefinite inner product space and generalized Krein space are introduced and some of their properties are obtained. Then the natural boundary of a \(p\) dissipative operator in Banach space is constructed and the maximal dissipative extension representation of a sort of \(p\) dissipative operators in Banach space by the natural boundary space is given. Finally, these results are used to study the relevant Schrödinger operator related to soliton wave and quantum mechanics.
Mathematics Subject Classification ID: 47B44
Mathematics Subject Classification ID: 46C50
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 46C20
zbMATH DE Number: 1334915
zbMATH Keywords: \(p\)-selfadjoint operators
zbMATH Keywords: generalized Schwartz inequality
zbMATH Keywords: maximal dissipative extension representation
zbMATH Keywords: \(p\)-dissipative operators
zbMATH Keywords: generalized semi-inner product space
zbMATH Keywords: generalized indefinite inner product space
zbMATH Keywords: generalized Krein space
zbMATH Keywords: natural boundary
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: soliton wave
MaRDI profile type: Publication
full work available at URL: s002200050567
OpenAlex ID: W2068858818
DOI: 10.1007/S002200050567
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description: scientific article; zbMATH DE number 1334915