On the duality of the symmetric strong diameter 2 property in Lipschitz spaces

AbstractFor any metric space X, the predual of Lip(X) is unique. If X has finite diameter or is complete and convex—in particular, if it is a Banach space—then the predual of Lip0(X) is unique.

Download Full-text

Lipschitz Spaces and Bernstein's Theorem on Absolutely Convergent Fourier Transforms*

Indiana University Mathematics Journal ◽

10.1512/iumj.1969.18.18024 ◽

1968 ◽

Vol 18 (4) ◽

pp. 283-323 ◽

Cited By ~ 11

Author(s):

C. Herz

Keyword(s):

Fourier Transforms ◽

Lipschitz Spaces

Download Full-text

Multiplier Representations of Sequence Spaces with Applications to Lipschitz Spaces and Spaces of Functions of Generalized Bounded Variation

Linear Spaces and Approximation / Lineare Räume und Approximation ◽

10.1007/978-3-0348-7180-8_22 ◽

1978 ◽

pp. 235-245

Author(s):

Günther Goes

Keyword(s):

Bounded Variation ◽

Sequence Spaces ◽

Lipschitz Spaces

Download Full-text

Some results on isometric composition operators on Lipschitz spaces

Revista Matemática Complutense ◽

10.1007/s13163-021-00410-1 ◽

2021 ◽

Author(s):

Abraham Rueda Zoca

Keyword(s):

Convex Hull ◽

Composition Operator ◽

Metric Spaces ◽

Composition Operators ◽

Extreme Points ◽

Necessary Condition ◽

Closed Convex Hull ◽

Lipschitz Spaces ◽

Complete Characterisation

AbstractGiven two metric spaces M and N we study, motivated by a question of N. Weaver, conditions under which a composition operator $$C_\phi :{\mathrm {Lip}}_0(M)\longrightarrow {\mathrm {Lip}}_0(N)$$ C ϕ : Lip 0 ( M ) ⟶ Lip 0 ( N ) is an isometry depending on the properties of $$\phi $$ ϕ . We obtain a complete characterisation of those operators $$C_\phi $$ C ϕ in terms of a property of the function $$\phi $$ ϕ in the case that $$B_{{\mathcal {F}}(M)}$$ B F ( M ) is the closed convex hull of its preserved extreme points. Also, we obtain necessary condition for $$C_\phi $$ C ϕ being an isometry in the case that M is geodesic.

Download Full-text