Local Spectral Theory for Operators R and S Satisfying RSR = R2
Palabras clave:
Local spectral subspace, Dunford’s property (C), operator equationResumen
We study some local spectral properties for bounded operators R, S, RS and SR in the case that R and S satisfy the operator equation RSR = R2. Among other results, we prove that S, R, SR and RS share Dunford’s property (C) when RSR = R2 and SRS = S2.
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Referencias
P. Aiena, “Fredholm and Local Spectral Theory, with Application to Multipliers”, Kluwer Acad. Publishers, Dordrecht, 2004.
P. Aiena, M. González, On the Dunford property (C) for bounded linear operators RS and SR, Integral Equations Operator Theory 70 (4) (2011), 561 – 568.
P. Aiena, M. Chō, M. González, Polaroid type operators under quasi-affinities, J. Math. Anal. Appl. 371 (2) (2010), 485 – 495.
P. Aiena, M.L. Colasante, M. González, Operators which have a closed quasi-nilpotent part, Proc. Amer. Math. Soc. 130 (9) (2002), 2701 – 2710.
B. Barnes, Common operator properties of the linear operators RS and SR, Proc. Amer. Math. Soc. 126 (4) (1998), 1055 – 1061.
C. Benhida, E.H. Zerouali, Local spectral theory of linear operators RS and SR Integral Equations Operator Theory 54 (1) (2006), 1 – 8.
T. Bermúdez, M. González, A. Martinón, Stability of the local spectrum Proc. Amer. Math. Soc. 125 (2) (1997), 417 – 425.
B.P. Duggal, Operator equations ABA = A2 and BAB = B2 , Funct. Anal. Approx. Comput. 3 (1) (2011), 9 – 18.
K.B. Laursen, M.M. Neumann, “An Introduction to Local Spectral Theory”, London Mathematical Society Monographs, New Series, 20, The Clarendon Press, New York, 2000.
C. Schmoeger, On the operator equations ABA = A2 and BAB = B2, Publ. Inst. Math, (Beograd) (N.S.) 78(92) (2005), 127 – 133.
C. Schmoeger, Common spectral properties of linear operators A and B such that ABA = A2 and BAB = B2, Publ. Inst. Math. (Beograd) (N.S.) 79(93) (2006), 109 – 114.
I. Vidav, On idempotent operators in a Hilbert space, Publ. Inst. Math. (Beograd) (N.S.) 4(18), (1964), 157 – 163.
Q. Zeng, H. Zhong, Common properties of bounded linear operators AC and BA: Local spectral theory, J. Math. Anal. Appl. 414 (2) (2014), 553 – 560.
