HILBERT-SCHMIDT INTERPOLATION ON AX = Y IN A TRIDIAGONAL ALGEBRA ALGL
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Given operators X and Y acting on a separable complex Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y . In this article, we investigate Hilbert-Schmidt interpolation problems for operators in a tridiagonal algebra and we get the following : Let L be a subspace lattice acting on a separable complex Hilbert space H and let X = (xij) and Y = (yij) be operators acting on H. Then the following are equivalent: (1) There exists a Hilbert-Schmidt operator A = (aij) in AlgL such that AX = Y . (2) There is a bounded sequence f®ng in C such that P1 n=1 j®nj2 < 1 and y1i = ®1x1i + ®2x2i y2k i = ®4k¡1x2k i y2k+1 i = ®4kx2k i + ®4k+1x2k+1 i + ®4k+2x2k+2 i for all i; k in N:
Abstract
Given operators X and Y acting on a separable complex Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y . In this article, we investigate Hilbert-Schmidt interpolation problems for operators in a tridiagonal algebra and we get the following : Let L be a subspace lattice acting on a separable complex Hilbert space H and let X = (xij) and Y = (yij) be operators acting on H. Then the following are equivalent: (1) There exists a Hilbert-Schmidt operator A = (aij) in AlgL such that AX = Y . (2) There is a bounded sequence f®ng in C such that P1 n=1 j®nj2 < 1 and y1i = ®1x1i + ®2x2i y2k i = ®4k¡1x2k i y2k+1 i = ®4kx2k i + ®4k+1x2k+1 i + ®4k+2x2k+2 i for all i; k in N:
참고문헌 (9)
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