Note on subnormal weighted shifts
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Abstract:
The purpose of this note is two-fold: (1) To point out that Stampfli’s characterization of subnormal shifts can be reformulated in operator form which turns out to be the Spitkovskii’s characterization of subnormal operators; (2) To use this reformulation to give a new proof of the subnormality of a class of shifts.References
- Carl C. Cowen and John J. Long, Some subnormal Toeplitz operators, J. Reine Angew. Math. 351 (1984), 216–220. MR 749683
- P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887–933. MR 270173, DOI 10.1090/S0002-9904-1970-12502-2
- Ji Pu Ma and Shao Jie Zhou, A necessary and sufficient condition for an operator to be subnormal, Nanjing Daxue Xuebao Shuxue Bannian Kan 2 (1985), no. 2, 258–267 (Chinese, with English summary). MR 834313
- I. M. Spitkovskiĭ, A criterion for the subnormalcy of operators in Hilbert space, Funktsional. Anal. i Prilozhen. 16 (1982), no. 2, 86–87 (Russian). MR 659177
- J. G. Stampfli, Which weighted shifts are subnormal?, Pacific J. Math. 17 (1966), 367–379. MR 193520
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 801-802
- MSC: Primary 47B20; Secondary 47B37
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947661-0
- MathSciNet review: 947661