Numerical Range on Weighted Hardy Spaces as Semi Inner Product Spaces

[1] A. Abdollahi and M. T. Heydari, Spatial Numerical Range of Operators on Weighted Hardy Spaces, International Journal of Mathematics and Mathematical Sciences. DOI:10.1155/2011/81268010.1155/2011/812680Open DOISearch in Google Scholar

[2] F. L. Bauer, On the Filed of Valuse Subordinates to a Norm, Numer. Math. 4 (1961) 103-111.10.1007/BF01386300Search in Google Scholar

[3] H.F. Bohnenblust, S. Karlin, Geometrical properties of the unit sphere in Banach algebra, Ann. Math. 62 (1955) 217-229.10.2307/1969676Search in Google Scholar

[4] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc. Lecture Notes Series 2, Cambridge, 1971.10.1017/CBO9781107359895Search in Google Scholar

[5] J. A. Clarkson, Uniformly Convex Spaces, Trans. Amer. Math. Soc. 40 (1936): 396-41410.1090/S0002-9947-1936-1501880-4Open DOISearch in Google Scholar

[6] C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, 1995Search in Google Scholar

[7] Elmouloudi Ed-dari, On the numerical index of Banach spaces, Linear Algebra and its Applications 403 (2005) 86-96.10.1016/j.laa.2005.01.012Search in Google Scholar

[8] E. A. Gallardo-Gutierrez and A. Montes-Rodriguez, The role of the spectrum in the cyclic behavior of composition operators, Mem. Amer. Math. Soc. 167 (2004), no. 791, x+81 pp.10.1090/memo/0791Search in Google Scholar

[9] B.W. Glickfeld, On an inequality of Banach algebra geometry and semiinner product space theory, Illinois J. Math. 14 (1970) 76-81.10.1215/ijm/1256053302Search in Google Scholar

[10] Gustafon, K. E., K. M. Rao.: The numerical range, the field of values of linear operators and matrices. Springer. New York. 1997.Search in Google Scholar

[11] L. P. Kuptsov, Hölder inequality, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, 2001, ISBN 978-1556080104.Search in Google Scholar

[12] K. Jahedi and B. Youseff, Numerical Range of Operators Acting on Banach Spaces, Czechoslovak Mathematical Journal, Vol. 62 (2012), No. 2, 495-503.10.1007/s10587-012-0024-7Open DOISearch in Google Scholar

[13] G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 1961 29-43.10.1090/S0002-9947-1961-0133024-2Open DOISearch in Google Scholar

[14] K. Seddighi, K. Hedayatiyan and B. Youseff, Operators acting on certain Banach spaces of analytic functions, Internat. J. Math. Math. Sci. 18 (1995), no. 1, 107-110.Search in Google Scholar

[15] A. L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, pp. 49-128. Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974.10.1090/surv/013/02Search in Google Scholar

[16] J. P. Williams, Spectra of Products and Numerical Ranges, J. Math. Anal. and Appl. 17 (1967) 214-220.10.1016/0022-247X(67)90146-1Open DOISearch in Google Scholar

[17] B. Youseff and S. Jahedi, Composition operators on Banach spaces of formal power series, Boll. Unione Math. Ital. Sez. B Artic. Ric. Mat. (8) 6 (2003), no. 2, 481-487.Search in Google Scholar

[18] N. Zorboska, Composition operators on S spaces, Indiana Univ. Math.Search in Google Scholar

J. 39 (1990), 847-857.Search in Google Scholar