My hidden notes

Submitted papers (journals)

30. On isometric embeddings into the set of strongly norm-attaining Lipschitz functions

(Submitted to Nonlinear Analysis (Q1))

(Submitted on 09-08-2022)

S.D., R. Medina, A. Quilis, and Ó. Roldán

(Submitted to Journal of the Institute of Mathematics of Jussieu (Q1))

(Submitted on 27-06-2022)

S.D. and R. Medina

(Submitted to Revista Matemática Complutense (Q2))

(Submitted on 25-05-2022)

S.D., P. Hájek, and T. Russo

(Submitted to Linear and Multilinear Algebra (Q1))

(Submitted on 10-03-2021)

S.D., S.K. Kim, H.J. Lee, and M. Mazzitelli

Under construction...

Lineability of the non-norm-attaining operators

S.D., J. Falcó, M. Jung, D. Rodríguez

On the Bollobás theorem for invariant groups

S.D., J. Falcó, M. Jung, Ó. Roldán


S.D., M. Jung, J.T. Rodríguez, M. Mazzitelli (2022)


w- and w^*-denseness of norm-attaining

G. Choi, S.D., M. Jung

Randon-Nikodým property and functions that attain their weighted norms

S.D., R. Medina

Open Problems

Strong Subdifferentiability

  • Is it true that the Banach space P(^2 \c_0, \K) endowed with the sup norm satisfies the sequential w^*-Kadec-Klee property? 
  • Is it true the following equivalence? For every Banach space X and Y, we have that X \pten Y is reflexive if and only X \pten Y is SSD

Daugavet and delta points

  • Is there a reflexive Banach space X such that P(^N X; \K) is reflexive and contains a Daugavet point? 


  • Is it possible to use lineability arguments to construct a very big Y of a nonseparable metric space M such that Y is inside \SNA(M)? 

Lipschitz-free spaces

  • Let T be the Tsirelson’ space. The space F(T) contains \ell_2? How about c_0?
  • The same question for James’ spaces.  


  • Does c_0 admite a renorming \|.\| such that (c_0, \|.\|) is a square space?

Daugavet property

  • The weighted Banach space H_v(X,Y) satisfies the Daugavet property?

Temas para estudiantes

Norm-attaining theory

  • Norm-attaining tensors and integral operators 
  • Anti-Bollobás
  • Local properties for compact operators and its relation with SSD