My hidden notes

Submitted papers (journals)

32. On the strong subdifferentiability of the homogeneous polynomials and (symmetric) tensor products

(Submitted)

S.D., M. Jung, M. Mazzitelli, and J.M. Rodríguez

On holomorphic functions attaining their weighted norms

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

(Submitted on 27-06-2022)

S.D. and R. Medina

Under construction...

11. Set points of discontinuity of hyperplanarly continuous maps on Banach spaces

S.D., Dani. Mirar:

 

  • A continuous tale on continuous and separatey continuous functions):
  • On sets of discontinuous of functions continuous on all lines: Zajicek

10. Funciones ES en espacios de sucesiones y funciones

S.D., Juanito

9. Non-norm attaining tensors (lineability)

S.D., Jaagup Kirme

8. Does the BPBp imply the BPBp for finite rank operators?

S.D., R. Medina

7. NA(J), where J is the James space

S.D., Jaagup Kirme

6. Norm attaining integral operators

S.D., M. Jung, M. Martín

5. Modes of convergence in nets

S.D., D. Rodríguez

4. Daugavet points in the homogenous polynomials spaces

R. J. Aliaga, S.D., M. Jung, A. Quilis, T. Veoorg

3. Lineability of the non-norm-attaining operators

S.D., J. Falcó, M. Jung, D. Rodríguez

2. On the Bollobás theorem for invariant groups

S.D., J. Falcó, M. Jung, Ó. Roldán

1. 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

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)? 

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.  

Renorming

  • 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