Weighted composition operators on Nachbin spaces with operator-valued weights
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Let $A$ be a normed space, $\mathcal B(A)$ the algebra of all bounded operators on $A$, and $V$ a family of strongly upper semicontinuous functions from a Hausdorff completely regular space $X$ into $\mathcal B(A)$. In this paper, we investigate some properties of the weighted spaces $CV(X, A)$ of all $A$-valued continuous functions $f$ on $X$ such that the mapping $x \mapsto v(x)(f(x))$ is bounded on $X$, for every $v \in V$, endowed with the topology generated by the seminorms $\|f\|_v = \sup\{\|v(x)(f(x))\| ,\ x \in X\}$. Our main purpose is to characterize continuous, bounded, and locally equicontinuous weighted composition operators between such spaces.
Abstract
Let $A$ be a normed space, $\mathcal B(A)$ the algebra of all bounded operators on $A$, and $V$ a family of strongly upper semicontinuous functions from a Hausdorff completely regular space $X$ into $\mathcal B(A)$. In this paper, we investigate some properties of the weighted spaces $CV(X, A)$ of all $A$-valued continuous functions $f$ on $X$ such that the mapping $x \mapsto v(x)(f(x))$ is bounded on $X$, for every $v \in V$, endowed with the topology generated by the seminorms $\|f\|_v = \sup\{\|v(x)(f(x))\| ,\ x \in X\}$. Our main purpose is to characterize continuous, bounded, and locally equicontinuous weighted composition operators between such spaces.
참고문헌 (31)
- K. D. Bierstedt, "Gewichtete Raume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. I", J. Reine Angew. Math, 259, pp.186~210 (1973)
- K. D. Bierstedt, "Tensor products of weighted spaces, in Function spaces and dense approximation (Proc. Conf., Univ. Bonn, Bonn, 1974)", Bonn. Math. Schriften, 81, pp.26~58 (1975), Inst. Angew. Math., Univ. Bonn
- K. D. Bierstedt, "Advances in the theory of Frechet spaces", pp.181~194 (1989), Kluwer Acad. Publ.
- K. D. Bierstedt, "Completeness of the (LB)-spaces V C(X)", Arch. Math. (Basel), 56(3), pp.281~285 (1991)
- K. D. Bierstedt, "Weighted (LF)-spaces of continuous functions", Math. Nachr, 165, pp.25~48 (1994)
- K. D. Bierstedt, "A projective description of weighted inductive limits", Trans. Amer. Math. Soc, 272(1), pp.107~160 (1982)
- J. Bonet, "On weighted inductive limits of spaces of continuous functions", Math. Z, 192(1), pp.9~20 (1986)
- J. Bonet, "Pointwise multiplication operators on weighted Banach spaces of analytic functions", Studia Math, 137(2), pp.177~194 (1999)
- J. Bonet, "A note on weighted Banach spaces of holomorphic functions", Arch. Math. (Basel), 81(6), pp.650~654 (2003)
- W. Govaerts, "Homomorphisms of weighted algebras of continuous functions", Ann. Mat. Pura Appl. (4), 116, pp.151~158 (1978)
- J. E. Jamison, "Weighted composition operator on C(X,E)", J. Operator Theory, 19(2), pp.307~317 (1988)
- J. S. Jeang, "Weighted composition operators of C0(X)'s", J. Math. Anal. Appl, 201(3), pp.981~993 (1996)
- L. A. Khan, "Operator-valued multiplication operators on weighted function spaces", Demonstratio Math, 35(3), pp.599~605 (2002)
- M. Klilou, "Multiplication operators on generalized weighted spaces of continuous functions", Mediterr. J. Math, 13(5), pp.3265~3280 (2016)
- K. Kour, "WCOs on non-locally convex weighted spaces of continuous functions", J. Indian Math. Soc. (N.S.), 66(1-4), pp.17~25 (1999)
- W. Lusky, "On the structure of Hv0(D) and hv0(D)", Math. Nachr, 159, pp.279~289 (1992)
- W. Lusky, "On weighted spaces of harmonic and holomorphic functions", J. London Math. Soc. (2), 51(2), pp.309~320 (1995)
- J. S. Manhas, "Weighted composition operators on nonlocally convex weighted spaces of continuous functions", Anal. Math, 24(4), pp.275~292 (1998)
- L. Nachbin, "Weighted approximation for algebras and modules of continuous functions:Real and self-adjoint complex cases", Ann. of Math. (2), 81, pp.289~302 (1965)
- L. Nachbin, "Elements of Approximation Theory" (1967), D. Van Nostrand Co., Inc.
- L. Oubbi, "Weighted algebras of continuous functions", Results Math, 24(3-4), pp.298~307 (1993)
- L. Oubbi, "On different types of algebras contained in CV (X)", Bull. Belg. Math. Soc. Simon Stevin, 6(1), pp.111~120 (1999)
- L. Oubbi, "Weighted composition operators on non-locally convex weighted spaces", Rocky Mountain J. Math, 35(6), pp.2065~2087 (2005)
- J. B. Prolla, "Weighted spaces of vector-valued continuous functions", Ann. Mat. Pura Appl. (4), 89, pp.145~157 (1971)
- J. B. Prolla, "Approximation of Vector Valued Functions" (1977), North-Holland Publishing Co.
- W. M. Ruess, "Compactness in spaces of vector valued continuous functions and asymptotic almost periodicity", Math. Nachr, 135, pp.7~33 (1988)
- C. Shekhar, "Multiplication operators on weighted spaces of continuous functions with operator-valued weights", Int. J. Contemp. Math. Sci, 7(37-40), pp.1889~1894 (2012)
- B. Singh, "On weighted composition operators on non-locally convex function spaces", Indian J. Pure Appl. Math, 28(11), pp.1505~1512 (1997)
- R. K. Singh, "Composition operators on weighted spaces of continuous functions", J. Austral. Math. Soc. Ser. A, 45(3), pp.303~319 (1988)
- W. H. Summers, "The general complex bounded case of the strict weighted approximation problem", Math. Ann, 192, pp.90~98 (1971)
- W. H. Summers, "The bounded case of the weighted approximation problem, in Functional analysis and applications (Proc. Sympos. Analysis, Univ. Fed. Pernambuco, Recife, 1972)", pp.177~183 (1974), Springer