Minimal Numerical-Radius Extensions of Operators

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Mathematics (CMC)

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In this paper we characterize minimal numerical-radius extensions of operators from finite-dimensional subspaces and compare them with minimal operator-norm extensions. We note that in the cases Lp, p = 1, ∞, and in the case of self-adjoint extensions in L2, the two extensions and their norms are equal.

An analogous result is also true for an arbitrary extension. Finally, we provide an example of a projection from l p3 onto a two-dimensional subspace which is minimal with respect to norm but not with respect to the numerical radius for p ≠ 1, 2,∞, and we determine the minimal numerical-radius projection in this same situation.

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© 2007 American Mathematical Society