Abstract
Bu çalışmasında Banach uzaylarda ki lineer sınırlı operatörler için s-sayı fonksiyonları üzerine bir araştırma yapılmıştır. Birinci bölümde s-sayı fonksiyonlarının gelişimi ve kullanıldığı yerler üzerine bilgi verilmiştir. İkinci bölümde bazı temel kavramlar hatırlatılmıştır. Üçüncü bölümde ise bazı önemli s-sayıları örnekleri verilmiştir. Ayrıca farklı operatörler için s-sayıları arasında ki bağıntılara yer verilmiştir. Böylece bir bütün olarak Banach uzaylarda s-sayılarının aksiyomatik teorisi sunulmuştur.
References
- Pietsch, A., s-Numbers of Operatorsin Banach Spaces, Studia Math., 1974, 51, 123-132.
- Pietsch, A., Eigenvalues and s-Numbers, Cambridge University Press., 1987.
- Pietsch, A., History of Banach Spaces and Linear Operators, Birkhauser Boston, 2007.
- König, H., Eigenvalues Distribution of Compact Operators. Operators Theory: Advances and Applications, 1986, (16), Birkauser, Basel.
- König, H., Eigenvalues of Operators and Aplication, Handbookof Geometry of Banach Spaces, North-Holland, Amsterdam, 2001, (1), 941-974.
- Ismailov, Z., Cona, L., ve Cevik E.O., Gelfand Numbers of Diagonal Matrices, Hacettepe Journal, 2015, Vol (44)1, 75-81.
- İpek Al, P. Lorentz-Schatten Classes ofDirect Sum of Operators, Hacettepe Journal of Mathematics and Statistics, 2020, cilt.49, ss.835-842.
Abstract
In this paper, a research on s-number functions for linear bounded operators in Banach spaces is studied. In the first chapter, information on the development of s-number functions and their usage is given. In the second part, some basic concepts are reminded. In the third part, some important examples of s-numbers are given. Also, the relations between s-numbers for different operators are given. Thus, the axiomatic theory of s-numbers in Banach spaces as a whole is presented
Keywords
References
- Pietsch, A., s-Numbers of Operatorsin Banach Spaces, Studia Math., 1974, 51, 123-132.
- Pietsch, A., Eigenvalues and s-Numbers, Cambridge University Press., 1987.
- Pietsch, A., History of Banach Spaces and Linear Operators, Birkhauser Boston, 2007.
- König, H., Eigenvalues Distribution of Compact Operators. Operators Theory: Advances and Applications, 1986, (16), Birkauser, Basel.
- König, H., Eigenvalues of Operators and Aplication, Handbookof Geometry of Banach Spaces, North-Holland, Amsterdam, 2001, (1), 941-974.
- Ismailov, Z., Cona, L., ve Cevik E.O., Gelfand Numbers of Diagonal Matrices, Hacettepe Journal, 2015, Vol (44)1, 75-81.
- İpek Al, P. Lorentz-Schatten Classes ofDirect Sum of Operators, Hacettepe Journal of Mathematics and Statistics, 2020, cilt.49, ss.835-842.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | REVIEWS |
| Authors | |
| Publication Date | March 8, 2022 |
| Submission Date | August 2, 2021 |
| Acceptance Date | November 12, 2021 |
| Published in Issue | Year 2022 Volume: 5 Issue: 1 |
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