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Let A(x) be a norm continuous family of bounded self-adjoint operators on a separable Hilbert space ℍ and let A(x)n be the orthogonal compressions of A(x) to the span of first n elements of an orthonormal basis of ℍ. The problem considered here is to approximate the spectrum of A(x) using the sequence of eigenvalues of A(x)n. We show that the bounds of the essential spectrum and the discrete spectral...
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