On 𝑝-hyponormal operators

Ko, Eungil

doi:10.1090/S0002-9939-99-05600-2

On $p$-hyponormal operators
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by Eungil Ko PDF

Proc. Amer. Math. Soc. 128 (2000), 775-780 Request permission

Abstract:

In this paper we show that $p$-hyponormal operators with $0 \notin \sigma (|T|_{r}^{\frac {1}{2}})$ are subscalar. As a corollary, we get that such operators with rich spectra have non-trivial invariant subspaces.

References

Ariyadasa Aluthge, On $p$-hyponormal operators for $0<p<1$, Integral Equations Operator Theory 13 (1990), no. 3, 307–315. MR 1047771, DOI 10.1007/BF01199886
Jörg Eschmeier, Invariant subspaces for subscalar operators, Arch. Math. (Basel) 52 (1989), no. 6, 562–570. MR 1007631, DOI 10.1007/BF01237569
Eungil Ko, On a Clary theorem, Bull. Korean Math. Soc. 33 (1996), no. 1, 29–33. MR 1386720
Mircea Martin and Mihai Putinar, Lectures on hyponormal operators, Operator Theory: Advances and Applications, vol. 39, Birkhäuser Verlag, Basel, 1989. MR 1028066, DOI 10.1007/978-3-0348-7466-3
Mihai Putinar, Hyponormal operators are subscalar, J. Operator Theory 12 (1984), no. 2, 385–395. MR 757441
Walter Rudin, Functional analysis, 2nd ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. MR 1157815
Daoxing Xia, Spectral theory of hyponormal operators, Operator Theory: Advances and Applications, vol. 10, Birkhäuser Verlag, Basel, 1983. MR 806959, DOI 10.1007/978-3-0348-5435-1