Journal of Operator Theory

Volume 33, Issue 1, Winter 1995 pp. 43-78.

Pure sub-Jordan operators and simultaneous approximation by a polynomial and its derivative

Authors: Joseph A. Ball (1) and Thomas R. Fanney (2)
Author institution:(1) Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, U.S.A.
(2) Department of Mathematics, Virginia Wesleyan College, Norfolk, VA 23502, U.S.A.

Summary: An operator T on a Hilbert space H is said to be Jordan (of order 2) if T = M + N where M*M = MM*, MN = NM and N^2 = 0, and to be sub-Jordan if T has an extension to a Jordan operator J on a larger Hilbert space $\mathcal K \supset \mathcal H$. If the sub-Jordan operator T is such that its minimal Jordan extension J has spectrum in the unit circle $\matbb T$ we say that T is $\mathbb T$-sub-Jordan. We present a functional model and solve an inverse spectral problem for this class of operators.

Keywords: Minimal Jordan extension, spectral measure, local resolvent, closed operator, annihilator.

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