Document Type: Research Paper

Author

Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.

Abstract

Let $(X,d)$ be an infinite compact metric space, let $(B,\parallel . \parallel)$ be a unital Banach space, and take $\alpha \in (0,1).$ In this work, at first we define the big and little $\alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $\alpha$-lipschitz $B$-valued operator algebra, $lip_{\alpha}(X,B)$. Then we characterize its second dual space.

Keywords

Main Subjects

###### ##### References

[1] A. Abdollahi, The maximal ideal space of analutic Lipschitz algebras, Rend. Circ. Mat. Palermo(2), 47 (1998), 347-352.

[2] D. Alimohammadi and A. Ebadian, Hedberg's theorem in real Lipschitz algebras, Indian J. Pure Appl. Math, 32 (2001), 1479-1493.

[3] H.X. Cao and Z.B. Xu, Some properties of Lipschitz-α operators, Acta Mathematica Sinica, Chinese Series, 45(2) (2002), 279-286.

[4] H.X. Cao, J.H. Zhang, and Z.B. Xu, Characterizations and Extensions of Lipschitz-α operators, Acta Mathematica Sinica, English Series, 22(3) (2006), 671-678.

[5] H.G. Dales, Banach algebras and Automatic Continuty, Clarendon Press. Oxford, 2000.

[6] A. Ebadian, Prime ideals in Lipschitz algebras of finite differentiable functions, Honam Math. J., 22 (2000), 21-30.

[7] T.G. Honary and H. Mahyar, Approximation in Lipschitz algebras, Quaest. Math., 23 (2000), 13-19.

[8] J.A. Johnson, Lipschitz spaces, Pacific J. Math., 51 (1975), 177-186.

[9] B. Pavlovic, Automatic continuity of Lipschitz algebras, J. Funct. anal. 131 (1995), 115-144.

[10] D.R. Sherbert, Banach algebras of Lipschitz functions, Pacific J. Math. 13 (1963), 1387-1399.

[11] N. Waver, Subalgebras of little Lipschitz algebras, Pacific J. Math., 173 (1996), 283-293.