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 $\mathbb T$ 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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