Abstract
In this chapter we further prepare the ground for the eigenvalue localization of elliptic global systems. Namely, in the following chapters we shall have to control the sandwitch (I –Π)B(I –Π) of an operator B, semi-bounded from below, by the orthogonal projectors (I –Π) relative to another operator A, semi-bounded from below. We present things in an abstract setting, for this is a useful machinery. Throughout this chapter H will always stand for a separable (infinite-dimensional) Hilbert space endowed with the scalar product (・, ・) = (・, ・)H.
Keywords
- Compact Operator
- Discrete Spectrum
- Bounded Linear Operator
- Hermitian Matrix
- Resolvent Operator
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Parmeggiani, A. (2010). On Operators Induced by General Finite-Rank Orthogonal Projections. In: Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction. Lecture Notes in Mathematics(), vol 1992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11922-4_10
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DOI: https://doi.org/10.1007/978-3-642-11922-4_10
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11921-7
Online ISBN: 978-3-642-11922-4
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