طیف و طیف اساسی ترکیبات خطی عملگرهای ترکیبی روی فضای هاردی H2
الموضوعات :محمود حاجی شعبانی 1 , مهسا فاتحی 2 , ملیحه فرضی 3
1 - استاد، دانشکده ریاضی، دانشگاه صنعتی شیراز، شیراز، ایران
2 - استاد، گروه ریاضی، واحد شیراز، دانشگاه آزاد اسلامی، شیراز، ایران
3 - دانشجوی دکتری، دانشکده ریاضی، دانشگاه صنعتی شیراز، شیراز، ایران
الکلمات المفتاحية: Hardy space, composition operator, Spectrum, essential spectrum,
ملخص المقالة :
فرض کنید ---. اگر--- یک خود نگاشت تحلیلی از --- باشد، برای هر --- تحلیلی روی ---، عملگر ترکیبی --- را به صورت --- تعریف کرده و --- را تابع ترکیب می‌نامیم.
[1] P. S. Bourdon, Spectra of some composition operators and associated weighted composition operators,J. OperatorTheory 67 (2012), 537-560.
[2] P. S. Bourdon, Spectra of composition operators with symbols in S(2), J. Operator Theory 75 (2016), 21-48.
[3] P. S. Bourdon and S. Narayan, Normal weighted composition operators on the Hardy space , J. Math. Anal. App. 367 (2010), 278-286.
[4] J. G. Caughran and H. J. Schwartz, Spectra of compact composition operators, Proc. Amer. Math. Soc. 51 (1975), 127-130.
[5] J. B. Conway, Functions of One Complex Variable, Second Edition, Springer-Verlag, New York, 1978.
[6] J. B. Conway, A Course in Functional Analysis, Second Edition, Springer-Verlag, New York, 1990.
[7] C. C. Cowen, Composition operators on , J. Operator Theory 9 (1983), 77-106.
[8] C. C. Cowen and E. Ko, Hermitian weighted composition operators on weighted Hardy spaces, Trans. Amer. Math. Soc. 362 (2010), 5771-5801.
[9] C. C. Cowen, E. Ko, D. Thompson and F. Tian, Spectra of some weighted composition operators on , Acta Sci. Math. (Szeged) 82 (2016), 221-234.
[10] C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions. Staudies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1995.
[11] J. A. Deddens, Analytic Toeplitz and composition operators, Canad. J. Math. 24 (1972), 859-865.
[12] M. Fatehi and M. Haji Shaabani, Certain nontrivially essentially self-adjoint weighted composition operators on H2 and A2, Complex Variables and Elliptic Equations. 59 (2014), 1626-1635.
[13] M. Fatehi and M. Haji Shaabani, Some essentially normal weighted composition operators on the weighted Bergman spaces, Complex Variables and Elliptic Equations. 60 (2015), 1205-1216.
[14] M. Fatehi and M. Haji Shaabani, Normal, cohyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces, Journal of the Korean Mathematical Society. 54 (2017), 599–612.
[15] M. Fatehi and M. Haji Shaabani, Norms of hyponormal weighted composition operators on the Hardy and weighted Bergman Spaces, Operators and Matrices. 12 (2018), 997–1007.
[16] M. Fatehi, M. Haji Shaabani and D. Thompson, Quasinormal and Hyponormal Weighted Composition Operators on H2 and A2 with Linear Fractional Compositional Symbol, Complex Anal. Oper. Theory, 12 (2018), 1767–1778.
[17] M. Fatehi, Complex symmetric weighted composition operators, Complex Variables and Elliptic Equations, to appear.
[18] G. Gunatillake, Spectrum of a compact weighted composition operator, Proc. Amer. Math. Soc. 135 (2) (2007), 461-467.
[19] G. Gunatillake, Invertible weighted composition operators, J. Funct. Anal. 261 (2011), 831-860.
[20] O. Hyvarinen, M. Lindstrom, I. Nieminen, and E. Saukko, Spectra of weighted composition operators with automorphic symbols, J. Funct. Anal. 265 (2013), 1749-1777.
[21] H. Kamowitz, The spectra of composition operators on , J. Funct. Anal.18 (1975),132-150.
[22] T. L. Kriete, B. D. MacCluer and J. L. Moorhouse, Toeplitz- composition -algebras, J. Operator Theory. 58 (2007), 135-156.
[23] R. Lim, L. H. Khoi, Complex symmetric weighted composition operators J. Math. Anal. Appl. 464 (2018), 101-118.
[24] S. K. Narayan, D. Sievewright and D. Thompson, Complex symmetric composition operators on H2, J. Math. Anal. Appl. 443 (2016), 625-630.
[25] E. A. Nordgren, Composition operators, Canad. J. Math. 20 (1968), 442-449.
[26] J. H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993.
[27] D. Thompson, Normaloid weighted composition operators on H2. Journal of Mathematical Analysis and Applications, 467 (2018), 1153-1162.
