Nevanlinna-Pick spaces with hyponormal multiplication operators

Hartz, Michael

doi:10.1090/S0002-9939-2015-12373-8

Nevanlinna-Pick spaces with hyponormal multiplication operators
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by Michael Hartz PDF

Proc. Amer. Math. Soc. 143 (2015), 2905-2912 Request permission

Abstract:

We show that the Hardy space on the unit disk is the only non-trivial irreducible reproducing kernel Hilbert space which satisfies the complete Nevanlinna-Pick property and hyponormality of all multiplication operators.

References

Jim Agler and John E. McCarthy, Complete Nevanlinna-Pick kernels, J. Funct. Anal. 175 (2000), no. 1, 111–124. MR 1774853, DOI 10.1006/jfan.2000.3599
Jim Agler and John E. McCarthy, Pick interpolation and Hilbert function spaces, Graduate Studies in Mathematics, vol. 44, American Mathematical Society, Providence, RI, 2002.
Călin-Grigore Ambrozie and Dan Timotin, On an intertwining lifting theorem for certain reproducing kernel Hilbert spaces, Integral Equations Operator Theory 42 (2002), no. 4, 373–384. MR 1885440, DOI 10.1007/BF01270919
William Arveson, Subalgebras of $C^*$-algebras. III. Multivariable operator theory, Acta Math. 181 (1998), no. 2, 159–228. MR 1668582, DOI 10.1007/BF02392585
Joseph A. Ball, Tavan T. Trent, and Victor Vinnikov, Interpolation and commutant lifting for multipliers on reproducing kernel Hilbert spaces, Operator theory and analysis (Amsterdam, 1997) Oper. Theory Adv. Appl., vol. 122, Birkhäuser, Basel, 2001, pp. 89–138. MR 1846055
L. E. J. Brouwer, Beweis der invarianz des $n$-dimensionalen gebiets, Math. Ann. 71 (1911), no. 3, 305–313 (German). MR 1511658, DOI 10.1007/BF01456846
John B. Garnett, Bounded analytic functions, 1st ed., Graduate Texts in Mathematics, vol. 236, Springer, New York, 2007. MR 2261424
Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 49–128. MR 0361899