Abstract
Aspects of the theory of mean ergodic operators and bases in Fréchet spaces were recently developed in [1]. This investigation is extended here to the class of barrelled locally convex spaces. Duality theory, also for operators, plays a prominent role.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A.A. Albanese, J. Bonet, W.J. Ricker, Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34 (2009), 1–37.
A.A. Albanese, J. Bonet, W.J. Ricker, Grothendieck spaces with the Dunford-Pettis property. Positivity, in press.
K.D. Bierstedt, R.G. Meise, W.H. Summers, Köthe sets and Köthe sequence spaces. In: “Functional Analysis, Holomorphy and Approximation Theory”, J.A. Barroso (Ed.), North-Holland, Amsterdam, 1982, pp. 27–91.
J. Bonet, W.J. Ricker, Schauder decompositions and the Grothendieck and Dunford-Pettis properties in Köthe echelon spaces of infinite order. Positivity 11 (2007), 77–93.
J.M.F. Castillo, J.C. Díaz, J. Motos, On the Fréchet space L p −. Manuscripta Math. 96 (1998), 219–230.
B. Cascales, J. Orihuela, On compactness in locally convex spaces. Math. Z. 195 (1987), 365–381.
J.C. Díaz, M.A. Miñarro, Distinguished Fréchet spaces and projective tensor product. Doĝa-Tr. J. Math. 14 (1990), 191–208.
N. Dunford, J.T. Schwartz, Linear Operators I: General Theory. 2nd Edition, Wiley-Interscience, New York, 1964.
R.E. Edwards, Functional Analysis. Reinhart and Winston, New York, 1965.
V.P. Fonf, M. Lin, P. Wojtaszczyk, Ergodic characterizations of reflexivity in Banach spaces. J. Funct. Anal. 187 (2001), 146–162.
N.J. Kalton, Schauder decompositions in locally convex spaces. Proc. Camb. Phil. Soc. 68 (1970), 377–392.
G. Köthe, Topological Vector Spaces I. 2nd Rev. Edition, Springer Verlag, Berlin-Heidelberg-New York, 1983.
G. Köthe, Topological Vector Spaces II. Springer Verlag, Berlin-Heidelberg-New York, 1979.
U. Krengel, Ergodic Theorems. Walter de Gruyter, Berlin, 1985.
M. Lin, On the uniform ergodic theorem. Proc. Amer. Math. Soc. 43 (1974), 337–340.
H.P. Lotz, Uniform convergence of operators on L ∞ and similar spaces. Math. Z. 190 (1985), 207–220.
R.G. Meise, D. Vogt, Introduction to Functional Analysis. Clarendon Press, Oxford, 1997.
G. Metafune, V.B. Moscatelli, On the space \( \ell ^{p + } = \cap _{q > p} \ell ^q \) . Math. Nachr. 147 (1990), 7–12.
S. Okada, Spectrum of scalar-type spectral operators and Schauder decompositions. Math. Nachr. 139 (1988), 167–174.
P. Pérez Carreras, J. Bonet, Barrelled Locally Convex Spaces. North Holland Math. Studies 131, Amsterdam, 1987.
K. Yosida, Functional Analysis. Springer Verlag, Berlin-Heidelberg, 1965.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Birkhäuser Verlag Basel/Switzerland
About this paper
Cite this paper
Albanese, A.A., Bonet, J., Ricker, W.J. (2009). On Mean Ergodic Operators. In: Curbera, G.P., Mockenhaupt, G., Ricker, W.J. (eds) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol 201. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0211-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-0346-0211-2_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0210-5
Online ISBN: 978-3-0346-0211-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)