Skip to main content Accessibility help
×
Home
Hostname: page-component-7f7b94f6bd-w6m4b Total loading time: 0.347 Render date: 2022-06-28T10:48:13.491Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP

Published online by Cambridge University Press:  02 August 2012

KEI JI IZUCHI
Affiliation:
Department of Mathematics, Niigata University, Niigata 950-2181, Japan e-mail: izuchi@m.sc.niigata-u.ac.jp
KOU HEI IZUCHI
Affiliation:
Department of Mathematics, Faculty of Education, Yamaguchi University, Yamaguchi 753-8511, Japan e-mail: izuchi@yamaguchi-u.ac.jp
YUKO IZUCHI
Affiliation:
Aoyama-Shinmachi 18-6-301, Nishi-ku, Niigata 950-2006, Japan e-mail: yfd10198@nifty.com
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let COP = 0H, where 0 is the little Bloch space on the open unit disk , and A() be the disk algebra on . For non-zero functions u1,u2,. . ., uNA() and distinct analytic self-maps ϕ12,. . .,ϕN satisfying ϕjA() and ∥ϕj=1 for every j, it is given characterisations of which the sum of weighted composition operators ∑Nj=1ujCϕj maps COP into A().

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

1.Chandra, H. and Singh, B., Compactness and norm of the sum of weighted composition operators on A(), Int. J. Math. Anal. (Ruse) 4 (2010), 19451956.Google Scholar
2.Cowen, C. and MacCluer, B., Composition operators on spaces of analytic functions (CRC Press, Boca Raton, FL, 1995).Google Scholar
3.Garnett, J., Bounded analytic functions (Academic Press, New York, 1981).Google Scholar
4.Gorkin, P., Decompositions of the maximal ideal space of L , Trans. Am. Math. Soc. 282 (1984), 3344.Google Scholar
5.Gorkin, P., Gleason parts and COP, J. Funct. Anal. 83 (1989), 4449.CrossRefGoogle Scholar
6.Hoffman, K., Bounded analytic functions and Gleason parts, Ann. Math. 86 (1967), 74111.CrossRefGoogle Scholar
7.Izuchi, K. and Ohno, S., Linear combinations of composition operators on H, J. Math. Anal. Appl. 378 (2008), 820839.CrossRefGoogle Scholar
8.Izuchi, K. and Ohno, S., Sums of weighted composition operators on H , J. Math. Anal. Appl. 384 (2011), 683689.CrossRefGoogle Scholar
9.Madigan, K. and Matheson, A., Compact composition operators on the Bloch space, Trans. Am. Math. Soc. 347 (1995), 26792687.CrossRefGoogle Scholar
10.Ohno, S., Differences of weighted composition operators on the disk algebra, Bull. Belg. Math. Soc. Simon Stevin 17 (2010), 101107.Google Scholar
11.Sarason, D., Algebras of functions on the unit circle, Bull. Am. Math. Soc. 79 (1973), 286299.CrossRefGoogle Scholar
12.Sarason, D., Functions of vanishing mean oscillation, Trans. Am. Math. Soc. 207 (1975), 391405.CrossRefGoogle Scholar
13.Sarason, D., The Shilov and Bishop decompositions of H + C, in Conference on harmonic analysis in honor of Antoni Zygmund, Chicago, IL, 1981, vols. I, II (Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983), 461474.Google Scholar
14.Shapiro, J., Composition operators and classical function theory (Springer-Verlag, New York, 1993).CrossRefGoogle Scholar
15.Smith, W., Compactness of composition operators on BMOA, Proc. Am. Math. Soc. 127 (1999), 27152725.CrossRefGoogle Scholar
16.Sundberg, C. and Wolff, T., Interpolating sequences for QAB, Trans. Am. Math. Soc. 276 (1983), 551581.Google Scholar
You have Access
1
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *