Operator-valued bases on Hilbert spaces

Journal of Linear and Topological Algebra

مقاله 2، دوره 02، شماره 04، اسفند 2013، صفحه 201-218   

نویسنده

M. S. Asgari^*

Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 13185-768, Tehran, Iran

چکیده

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obtain some characterizations of them. We study orthonormal and Riesz ov-bases for Hilbert spaces. Finally we consider the stability of ov-bases under small perturbations. We generalize a result of Paley-Wiener [4] to the situation of ov-basis.

کلیدواژه‌ها

ov-bases؛ dual ov-bases؛ Bessel ov-bases؛ Hilbert ov-bases؛ ov-biorthogonal sequence

مراجع

[1] M. S. Asgari, H. Rahimi, Generalized frames for operators in Hilbert spaces, Inf. Dim. Anal. Quant. Probab. Rel. Topics, Vol. 17, No. 2, (2014), 1450013-1 - 1450013-20.

[2] W. Rudin, Functional Analysis,McGrawHill. Inc, New York, (1991).

[3] W. Sun, G-frames and G-Riesz bases, J. Math. Anal. Appl. (2006), 322, 437-452.

[4] R. Young, An Introduction to Nonharmonic Fourier Series, Academic Press, New York, (2001).