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

Phi-properties

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

↓↓↓ IDEAS FOR THE FUTURE ↓↓↓

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

Anti-Bollobás

S.D. 

Norm-attaining tensors and integral operators 

S.D.

Every reflexive projective tensor product is SSD

S.D.

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? 

Lineability

  • 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)? 

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