WEYL'S TYPE THEOREMS FOR ALGEBRAICALLY (p, k)-QUASIHYPONORMAL OPERATORS
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If $T^*$ is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$, where $Hol({\sigma}(T))$ is the space of all functions that analytic in an open neighborhoods of ${\sigma}(T)$ of T. (c) If $T^*$ is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$. (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum $\sigma_{SBF_+^-}(T)$, and for left Drazin spectrum ${\sigma}_{lD}(T)$ for every $f{\in}Hol({\sigma}T))$.
Abstract
For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If $T^*$ is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$, where $Hol({\sigma}(T))$ is the space of all functions that analytic in an open neighborhoods of ${\sigma}(T)$ of T. (c) If $T^*$ is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$. (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum $\sigma_{SBF_+^-}(T)$, and for left Drazin spectrum ${\sigma}_{lD}(T)$ for every $f{\in}Hol({\sigma}T))$.
참고문헌 (36)
- P. Aiena, "Fredholm and Local Spectral Theory with Applications to Multipliers" (2004), Kluwer
- P. Aiena, "The single valued extension property and the generalized Kato decomposition property", Acta Sci. Math, 67(3-4), pp.791~807 (2001)
- M. Amouch, "On the equivalence of Browder's and generalized Browder's theorem", Glasg. Math. J, 48(1), pp.179~185 (2006)
- S. K. Berberian, "An extension of Weyl's theorem to a class of not necessarily normal operators", Michigan Math. J, 16, pp.273~279 (1969)
- S. K. Berberian, "The Weyl spectrum of an operator", Indiana Univ. Math. J, 20, pp.529~544 (1970)
- M. Berkani, "On a class of Quasi-Fredholm operators", Integral Equations Operator Theory, 34(2), pp.244~249 (1999)
- M. Berkani, "Index of B-Fredholm operators and generalization of a Weyl theorem", Proc. Amer. Math. Soc, 130(6), pp.1717~1723 (2002)
- M. Berkani, "B-Weyl spectrum and poles of the resolvent", J. Math. Anal. Appl, 272(2), pp.596~603 (2002)
- M. Berkani, "Generalized weyl's theorem and hyponormal operators", J. Aust. Math. Soc, 76(2), pp.1~12 (2004)
- M. Berkani, "Weyl type theorems for bounded linear operators", Acta Sci. Math, 69(1-2), pp.359~376 (2003)
- M. Berkani, "An Atkinson-type theorem for B-Fredholm operators", Studia Math, 148(3), pp.251~257 (2001)
- L. A. Coburn, "Weyl's theorem for nonnormal operators", Michigan Math. J, 13, pp.285~288 (1966)
- R. E. Curto, "Weyl's theorem for algebraically paranormal operators", Integral Equations Operator Theory, 47(3), pp.307~314 (2003)
- H. R. Dowson, "Spectral Theory of Linear Operators" (1978), Academic Press
- B. P. Duggal, "Generalized Weyl's theorem for a class of operators satisfying a norm condition", Proc. Roy. Irish Acad. Sect. A, 104(1), pp.271~277 (2004)
- B. P. Dugga, "Generalised Weyl's theorem for a class of operators satisfying a norm condition", Math. Proc. R. Ir. Acad, 104(1), pp.75~81 (2004)
- J. K. Finch, "The single valued extension property on a Banach space", Pacic J. Math, 58(1), pp.61~69 (1975)
- R. E. Harte, "Invertibility and Singularity for Bounded Linear Operators" (1988), Marcel Dekker
- S. H. Lee, "On Weyl's theorem II", Math. Japon, 43(3), pp.549~553 (1996)
- A.-H. Kim, "Weyl's theorem for isoloid and reguloid operators", Commun. Korean Math. Soc, 14(1), pp.179~188 (1999)
- I. H. Kim, "On (p, k)-quasihyponormal operators", Math. Inequal. Appl, 7(4), pp.629~638 (2004)
- J. J. Koliha, "Isolated spectral points", Proc. Amer. Math. Soc, 124(11), pp.3417~3424 (1996)
- M. Lahrouz, "Weyl type theorems and the approximate point spectrum", Irish Math. Soc. Bull, 55, pp.41~51 (2005)
- K. B. Laursen, "Operators with nite ascent", Pacic J. Math, 152(2), pp.323~336 (1992)
- S. Mecheri, "Weyl's theorem for algebraically (p; k)-quasihyponormal operators", Georgian Math. J, 13(2), pp.307~313 (2006)
- V. Rako, "Operators obeying a-Weyl's theorem", Rev. Roumaine Math. Pures Appl, 34(10), pp.915~919 (1989)
- V. Rako, "Semi-Fredholm operators with nite ascent or descent and perturbation", Proc. Amer. Math. Soc, 122(12), pp.3823~3825 (1995)
- V. Rako, "Semi-Browder operators and perturbations", Studia Math, 122(2), pp.131~137 (1997)
- V. Rako, "Operators Obeying a-Weyl's theorem", Publ. Math. Debrecen, 55(3-4), pp.283~298 (1999)
- M. H. M. Rashid, "Weyl's type theorems for quasi- Class A operators", J. Math. Stat, 4(2), pp.70~74 (2008)
- M. H. M. Rashid, "Generalized Weyl's theorem for log-hyponormal", Malaysian J. Math. Soc, 2(1), pp.73~82 (2008)
- C. Schmoeger, "On operators T such that Weyl's theorem holds for f(T)", Extracta Math, 13(1), pp.27~33 (1998)
- K. Tanahashi, "Isolated point of spectrum of (p; k)- quasihyponormal operators", Linear Algebra Appl, 382(1), pp.221~229 (2004)
- A. E. Taylor, "Theorems on ascent, descent, nullity and defect of linear operators", Math. Ann, 163, pp.18~49 (1966)
- H. Weyl, "Uber beschrankte quadratische Formen, deren Differenze vollsteting ist", Rend. Circ. Math. Palermo, 27, pp.373~392 (1909)
- M. Berkani, "On the equivalence of Weyl theorem and generalized Weyl theorem", Acta Math. Sin, 23(1), pp.103~110 (2007)