Metric spaces with linear extensions preserving Lipschitz condition

Metric Embeddings and Lipschitz Extensions

Linear operators of Banach spaces with range in Lipschitz algebras

In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.

Spaces of Lipschitz Functions on Metric Spaces

In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.

Norm Preserving Extensions of Linear Transformations on Hilbert Spaces

Introduction. Let 77 be a Hubert space and let D be a closed proper subspace of 77. Let 70 be a linear contraction on D to 77. The problem of characterizing the contractions on all of 77 which extend J0 is directly related to the extension problems for unbounded transformations posed and treated by M. G. Krein [2] and R. S. Phillips [3]. In §1 of this paper we establish the following solution o...

Infinitesimally Lipschitz Functions on Metric Spaces

For a metric space X, we study the space D∞(X) of bounded functions on X whose infinitesimal Lipschitz constant is uniformly bounded. D ∞(X) is compared with the space LIP∞(X) of bounded Lipschitz functions on X, in terms of different properties regarding the geometry of X. We also obtain a Banach-Stone theorem in this context. In the case of a metric measure space, we also compare D∞(X) with t...