Harnack’s theorem for harmonic compact operator-valued functions
نویسندگان
چکیده
In this paper we show that harmonic compact operator-valued functions are characterized by having harmonic diagonal matrix coefficients in any choice of basis. We also give an example which shows that an operator-valued function with values outside the compact operators can have harmonic diagonal matrix coefficients in any choice of basis without being a harmonic operator-valued function. We use our harmonic matrix coefficients characterization to establish a Harnack’s theorem for an increasing sequence of harmonic compact self-adjoint operator-valued functions and we show that this Harnack’s theorem need not hold when the compactness restriction is dropped. © 2001 Elsevier Science Inc. All rights reserved.
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