Some spectral results for certain positive operators in Hilbert spaces

Abstract

This paper examines the spectral properties of specific classes of positive operators arising from matrices associated with the linear complementarity problem. Such operators occupy a central position in diverse domains of mathematics and physics, including operator theory, functional analysis, and quantum mechanics. A thorough understanding of their spectral behavior is fundamental for exploring the dynamics and stability of systems governed by these operators. P-matrix is one of the important types of matrices appearing in linear complementarity problems. In this paper, with the help of spectral results we have given a factorization for P-matrices, as the product of two non-trivial P-matrices. We also focus on elucidating spectral properties such as eigenvalues, approximate eigenvalues and spectral values associated with certain positive operators.

Key words: Spectrum of bounded operator, P-matrix, sufficient matrix, P-operator, positive definite operator.

Full Text

Article Information

Title	Some spectral results for certain positive operators in Hilbert spaces
Source	Methods Funct. Anal. Topology, Vol. 32 (2026), no. 1, 84-96
DOI	10.31392/MFAT-npu26_1.2026.09
Milestones	Received 05/06/2025; Revised 16/09/2025
Copyright	The Author(s) 2026 (CC BY-SA)

Authors Information

Rashid A.
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka (NITK), Surathkal, Mangaluru, Karnataka 575025, India

P. Sam Johnson
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka (NITK), Surathkal, Mangaluru, Karnataka 575025, India

Citation Example

Rashid A. and P. Sam Johnson, Some spectral results for certain positive operators in Hilbert spaces, Methods Funct. Anal. Topology 32 (2026), no. 1, 84-96.

BibTex

@article {MFAT2214,
    AUTHOR = {Rashid A. and P. Sam Johnson},
     TITLE = {Some spectral results for certain positive operators in Hilbert spaces},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {32},
      YEAR = {2026},
    NUMBER = {1},
     PAGES = {84-96},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_1.2026.09},
       URL = {https://mfat.imath.kiev.ua/article/?id=2214},
}

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