Abstract
In this chapter we study basic properties of compact operators on Banach spaces. We present the elementary spectral theory of compact operators in Banach spaces, including the spectral radius and properties of eigenvalues. Then we discus basic spectral properties of selfadjoint operators on Hilbert spaces, their spectral decomposition, and show some of the applications of these topics.
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S. Argyros and R. Haydon, A hereditarily indecomposable \(L_\infty\)-space that solves the scalar-plus-compact problem, submitted March 23rd, 2009. arXiv:0903.3921v2 [math.FA]
P. Enflo, On the invariant subspace problem for Banach spaces, Acta Math. 158, (1987), 213–313 (submitted in 1981).
G.J. Murphy, C *-algebras and operator theory, Academic Press, 1996.
C. Read, A solution to the invariant subspace problem on the space ℓ 1. Bull. London Math. Soc. 17 (1985), 305–317.
W. Rudin, Real and complex analysis, McGraw Hill, New York, 1974.
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Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V. (2011). Compact Operators on Banach Spaces. In: Banach Space Theory. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7515-7_15
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DOI: https://doi.org/10.1007/978-1-4419-7515-7_15
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