The Functional-Analytic Properties of the Limit q-Bernstein Operator
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-08
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
The limit q-Bernstein operator Bq, 0 The latter is used in the q-boson theory to describe the energy distribution in a q-analogue of the coherent state. Lately, the limit q-Bernstein operator has been widely under scrutiny, and it has been shown that Bq is a positive shape-preserving linear operator on C[0,1] with ∥Bq∥=1. Its approximation properties, probabilistic interpretation, eigenstructure, and impact on the smoothness of a function have been examined. In this paper, the functional-analytic properties of Bq are studied. Our main result states that there exists an infinite-dimensional subspace M of C[0,1] such that the restriction Bq|M is an isomorphic embedding. Also we show that each such subspace M contains an isomorphic copy of the Banach space c0.
American Psychological Association (APA)
Ostrovska, Sofiya. 2012. The Functional-Analytic Properties of the Limit q-Bernstein Operator. Journal of Function Spaces،Vol. 2012, no. 2012, pp.1-8.
https://search.emarefa.net/detail/BIM-994303
Modern Language Association (MLA)
Ostrovska, Sofiya. The Functional-Analytic Properties of the Limit q-Bernstein Operator. Journal of Function Spaces No. 2012 (2012), pp.1-8.
https://search.emarefa.net/detail/BIM-994303
American Medical Association (AMA)
Ostrovska, Sofiya. The Functional-Analytic Properties of the Limit q-Bernstein Operator. Journal of Function Spaces. 2012. Vol. 2012, no. 2012, pp.1-8.
https://search.emarefa.net/detail/BIM-994303
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-994303