/pdf/positive-off-diagonal-operators-on-ordered-normed-spaces-and-1ywpfwk7k3.pdf

Positive-off-diagonal Operators on Ordered Normed Spaces and Maximum Principles for M-Operators

The equation 
$$Ax = y$$

 for a positive linear continuous operator is considered in an ordered normed space 
$$\left( {X,K,\left\| \cdot \right\|} \right)$$

 , where the cone is assumed to be closed and having a nonempty interior. Then the dual cone 
$$K'$$

 of K possesses a base 
$${\mathcal{F}}$$

 . Generalizing the well known maximum principle for positive matrices an operator A is said to satisfy the maximum principle, if for any 
$$x \in K,\;x \ne 0$$

 there exists a positive linear continuous functional 
$$f \in {\mathcal{F}}$$

 which is both, maximal on the element Ax, i.e. 
$$f\left( {Ax} \right) = \sup _{g \in {\mathcal{F}}} g\left( {Ax} \right)$$

 , and positive on the element x, i.e. 
$$f\left( x \right) >0$$

 . This property is studied and characterized both analytically by some extreme point condition and geometrically by means of the behaviour under A of the faces of the cone K. It is shown that the conditions which have been obtained for finite dimensional spaces in earlier relevant papers are special cases of conditions presented in this paper. The maximum pinciple is proved for simple operators in the spaces 
$$C\left[ {0,1} \right]$$

 and c.

On a certain Maximum Principle for Positive Operators in an Ordered Normed Space

On maximum principles for M-operators

Positive-o-diagon al Operators on Ordered Normed Spaces and Maximum Principles for M-Operators

On matrices satisfying a maximum principle with respect to a cone

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

W. Schirotzek

Author Tools

Chat about Author

Papers

On matrices satisfying a maximum principle with respect to a cone