Titlebook: Topics in Operator Theory; Constantin Apostol M I. Gohberg (Raymond and Beverly Sackler Faculty of Book 1988 Springer Basel AG 1988 analysi

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Stability of Invariant Lagrangian Subspaces I,ons of the matrix or the operator, attracted much attention (see [BGK, GR, GLR1, AFS]). The main motivation to consider these problems comes from factorizations of matrix and operator functions, where invariant subspaces appear as the main tool in describing the factorizations (for this approach to factorization see, e.g., [BGK, GLR2]).

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On the Four Block Problem, I, the kind studied in [1]. The main theoretical fact proven here is an explicit closed form formula for the essential norm of the four block operator (see Proposition 1.1). We dedicate this paper to the memory of Constantin Apostol who was a great master of the essential properties of operators in Hilbert space.

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