Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We present two new forms in which the Fréchet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant C(T) : A → [A, T]. Then we apply the results to study series of vector-valued functions on domains in Banach spaces and to the analytic functional calculus in a complex Banach space.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
155--177
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Dipartimento di Matematica Pura ed Applicata via Trieste, 63, 35121 Padova, Italy, silvestr@math.unipd.it
Bibliografia
- [1] N. Bourbaki, General topology, Part 1, Part 2, Springer-Verlag, 1989.
- [2] N. Bourbaki, Functions of a real variable, Springer-Verlag, 2003.
- [3] N. Bourbaki, Lie Groups and Lie Algebras. Chapters 1–3, Springer-Verlag, 1989.
- [4] N. Bourbaki, Integration I,II, Springer-Verlag, 2003.
- [5] V.I. Burenkov, The formula for the differentiation of functions of operators that depend on a parameter, Mat. Zametki 10 (1971), 207–218.
- [6] H.G. Dales, Banach Algebras and Automatic Continuity, Mathematical Society Monographs, London, 2000.
- [7] J. Dieudonne’, Foundations of Modern Analysis 1, Academic Press, 1969.
- [8] N. Dunford, J.T. Schwartz, Linear operators, vol 1, 2, 3, Wiley Interscience, 1988.
- [9] T.M. Flett, Differential Analysis, Cambridge University Press, 1980.
- [10] R.S. Martin, Thesis, California Institute of Technology, 1932.
- [11] A.D. Michal, The Frech´et differentials of regular power series in normed linear spaces, Duke Math. J. 13 (1946), 57–59.
- [12] T.W. Palmer, Banach Algebras and The General Theory of ∗Algebras, vol 1, Cambridge University Press, 1994.
- [13] W. Rudin, Functional Analysis, McGraw-Hill, 1973.
- [14] A.C. Schaeffer, Inequalities of A. Markoff and S. Bernstein for polynomials and related functions, Bull. Amer. Math. Soc. 47 (1941), 565–579.
- [15] L. Schwartz, Analyse, I-IV, Hermann, 1993.
- [16] B. Silvestri, Integral equalities for functions of unbounded spectral operators in Banach spaces, Dissertationes Math. 464 (2009), 60 pp. http://dx.doi.org/10.4064/dm464-0-1 ArXiv.org http://arxiv.org/abs/0804.3069.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0002-0021