Functional Calculus Extensions on Dual Spaces
نویسنده
چکیده
In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply this result to give some sufficient conditions for an operator with an absolutely continuous functional calculus to admit a bounded Borel one.
منابع مشابه
Extensions of an Ac(σ) Functional Calculus
On a reflexive Banach space X , if an operator T admits a functional calculus for the absolutely continuous functions on its spectrum σ(T ) ⊆ R, then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can constru...
متن کاملA finite element exterior calculus framework for the rotating shallow-water equations
6 We describe discretisations of the shallow water equations on the sphere using the framework of finite element exterior calculus, which are extensions of the mimetic finite difference framework presented in Ringler, Thuburn, Klemp, and Skamarock (Journal of Computational Physics, 2010). The exterior calculus notation provides a guide to which finite element spaces should be used for which phy...
متن کاملSTABILITY OF THE JENSEN'S FUNCTIONAL EQUATION IN MULTI-FUZZY NORMED SPACES
In this paper, we define the notion of (dual) multi-fuzzy normedspaces and describe some properties of them. We then investigate Ulam-Hyers stability of Jensen's functional equation for mappings from linear spaces into multi-fuzzy normed spaces. We establish an asymptotic behavior of the Jensen equation in the framework of multi-fuzzy normed spaces.
متن کاملGeometric Aspects of Discretized Classical Field Theories: Extensions to Finite Element Exterior Calculus, Noether Theorems, and the Geodesic Finite Element Method
OF THE DISSERTATION Geometric Aspects of Discretized Classical Field Theories: Extensions to Finite Element Exterior Calculus, Noether Theorems, and the Geodesic Finite Element Method by Joe Salamon Doctor of Philosophy in Physics University of California San Diego, 2016 Professor Melvin Leok, Chair Professor Michael Holst, Co-Chair In this dissertation, I will discuss and explore the various t...
متن کاملOn certain fractional calculus operators involving generalized Mittag-Leffler function
The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...
متن کامل