THERMAL SCIENCE
International Scientific Journal
POINT SPECTRUM, RESIDUAL SPECTRUM, AND CONTINUOUS SPECTRUM OF UNBOUNDED UPPER TRIANGULAR OPERATOR MATRICES
ABSTRACT
This paper examines the completion of the point spectrum, residual spectrum, and continuous spectrum of an unbounded operator matrix acting in a Hilbert space. The necessary and sufficient conditions for the point spectrum of an unbounded operator matrix to be equal to the union of the point spectra of its diagonal entries are presented.
KEYWORDS
PAPER SUBMITTED: 2024-05-07
PAPER REVISED: 2024-07-10
PAPER ACCEPTED: 2024-07-10
PUBLISHED ONLINE: 2025-07-06
THERMAL SCIENCE YEAR
2025, VOLUME
29, ISSUE
Issue 3, PAGES [1811 - 1820]
- Du, H., Pan, J., Perturbation of Spectrum of 2 x 2 Operator Matrices, Proceedings of the American Mathematical Society, 121 (1994), 3, pp. 761-766
- Han, J., et al., W. Y., Invertible Completions of 2 x 2 Upper Triangular Operator Matrices, Proceedings of the American Mathematical Society, 128 (1999), 1, pp. 119-123
- Kuo, P. H., et al., A Thermal Displacement Prediction System with an Automatic LRGTVAC-PSO Optimized Branch Structured Bidirectional GRU Neural Network, IEEE Sensors Journal, 23 (2023), 12, pp. 12574-12586
- Kuo, P. H., et al., Thermal Displacement Prediction Model with a Structural Optimized Transfer Learning Technique, Case Studies in Thermal Engineering, 49 (2023), 103323
- Djordjevic, D., Perturbations of Spectra of Operator Matrices, Journal of Operator Theory, 48 (2002), 3, pp. 467-486
- Hai, G., Chen, A., On the Right (Left) Invertible Completions for Operator Matrices, Integral Equations Operator Theory, 67 (2010), Mar., pp. 79-93
- Zhang, S., Wu, Z., Characterizations of Perturbations of Spectra of 2 x 2 Upper Triangular Operator Matrices, Journal of Mathematical Analysis and Applications, 392 (2012), 2, pp. 103-110
- Zhang, S., et al., Continuous Spectrum, Point Spectrum and Residual Spectrum of Operator Matrices, Linear Algebra and its Applications, 433 (2010), 3, pp. 653-661
- Hai, G., Chen, A., The Residual Spectrum and the Continuous Spectrum of Upper Triangular Operator Matrices, Filomat, 28 (2014), 1, pp. 65-71
- Chen, A., et al., Spectra of 2 x 2 Upper Triangular Operator Matrices with Unbounded Entries (In Chinese), Scientia Sinica Mathematica, 46 (2016), 2, pp. 157-168
- Elbjaoui, H., Zerouali, E. H., Operator Matrices, International Journal of Mathematics, 42 (2003), July, pp. 2667-2672