An asymmetric Putnam–Fuglede theorem for unbounded operators

Stochel, Jan

doi:10.1090/S0002-9939-01-06127-5

An asymmetric Putnam–Fuglede theorem for unbounded operators
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by Jan Stochel

Proc. Amer. Math. Soc. 129 (2001), 2261-2271

DOI: https://doi.org/10.1090/S0002-9939-01-06127-5

Published electronically: March 20, 2001

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Abstract:

The intertwining relations between cosubnormal and closed hyponormal (resp. cohyponormal and closed subnormal) operators are studied. In particular, an asymmetric Putnam–Fuglede theorem for unbounded operators is proved.

References

Kevin Clancey, Seminormal operators, Lecture Notes in Mathematics, vol. 742, Springer, Berlin, 1979. MR 548170, DOI 10.1007/BFb0065642
Takayuki Furuta, On relaxation of normality in the Fuglede-Putnam theorem, Proc. Amer. Math. Soc. 77 (1979), no. 3, 324–328. MR 545590, DOI 10.1090/S0002-9939-1979-0545590-2
Takayuki Furuta, An extension of the Fuglede-Putnam theorem to subnormal operators using a Hilbert-Schmidt norm inequality, Proc. Amer. Math. Soc. 81 (1981), no. 2, 240–242. MR 593465, DOI 10.1090/S0002-9939-1981-0593465-4
Jan Janas, On unbounded hyponormal operators, Ark. Mat. 27 (1989), no. 2, 273–281. MR 1022281, DOI 10.1007/BF02386376
Jan Janas, On unbounded hyponormal operators. II, Integral Equations Operator Theory 15 (1992), no. 3, 470–478. MR 1155715, DOI 10.1007/BF01200330
J. Janas, On unbounded hyponormal operators. III, Studia Math. 112 (1994), no. 1, 75–82. MR 1307601, DOI 10.4064/sm-112-1-75-82
Kyung Hee Jin, On unbounded subnormal operators, Bull. Korean Math. Soc. 30 (1993), no. 1, 65–70. MR 1217370
R. L. Moore, D. D. Rogers, and T. T. Trent, A note on intertwining $M$-hyponormal operators, Proc. Amer. Math. Soc. 83 (1981), no. 3, 514–516. MR 627681, DOI 10.1090/S0002-9939-1981-0627681-X
Sch\B{o}ichi Ōta, Closed linear operators with domain containing their range, Proc. Edinburgh Math. Soc. (2) 27 (1984), no. 2, 229–233. MR 760619, DOI 10.1017/S0013091500022331
Sch\B{o}ichi Ōta, A quasi-affine transform of an unbounded operator, Studia Math. 112 (1995), no. 3, 279–284. MR 1311703, DOI 10.4064/sm-112-3-279-284
Sch\B{o}ichi Ōta and Konrad Schmüdgen, On some classes of unbounded operators, Integral Equations Operator Theory 12 (1989), no. 2, 211–226. MR 986595, DOI 10.1007/BF01195114
Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
C. R. Putnam, Ranges of normal and subnormal operators, Michigan Math. J. 18 (1971), 33–36.
M. Radjabalipour, Ranges of hyponormal operators, Illinois J. Math. 21 (1977), no. 1, 70–75. MR 448140, DOI 10.1215/ijm/1256049502
Mehdi Radjabalipour, On majorization and normality of operators, Proc. Amer. Math. Soc. 62 (1976), no. 1, 105–110 (1977). MR 430851, DOI 10.1090/S0002-9939-1977-0430851-6
Zoltán Sebestyén, On ranges of adjoint operators in Hilbert space, Acta Sci. Math. (Szeged) 46 (1983), no. 1-4, 295–298. MR 739046
Joseph G. Stampfli and Bhushan L. Wadhwa, An asymmetric Putnam-Fuglede theorem for dominant operators, Indiana Univ. Math. J. 25 (1976), no. 4, 359–365. MR 410448, DOI 10.1512/iumj.1976.25.25031
Joseph G. Stampfli and Bhushan L. Wadhwa, On dominant operators, Monatsh. Math. 84 (1977), no. 2, 143–153. MR 458225, DOI 10.1007/BF01579599
J. Stochel, Lifting strong commutants of unbounded subnormal operators, preprint 1999.
Joachim Weidmann, Linear operators in Hilbert spaces, Graduate Texts in Mathematics, vol. 68, Springer-Verlag, New York-Berlin, 1980. Translated from the German by Joseph Szücs. MR 566954, DOI 10.1007/978-1-4612-6027-1
Takashi Yoshino, Remark on the generalized Putnam-Fuglede theorem, Proc. Amer. Math. Soc. 95 (1985), no. 4, 571–572. MR 810165, DOI 10.1090/S0002-9939-1985-0810165-7