34. Algebraic genericity of certain families of nets in Functional Analysis

*(Submitted on 2024-01-15 to Israel J. Math.)*

**S.D. **and Rodríguez-Vidanes

33. NA lineability

*(Submitted on 2023-11-29 to Adv Math)*

**S.D.**, J. Falcó, M. Jung, D. Rodríguez-Vidanes

*Ideas for FUTURE projects*

Mirar las diapositivas de Miguel de la Winter School Korea 2024

★ To find (norm-attaining) operators which belong to the subset BŠ(X,Y) and then study its denseness

The same question can be done for its complement. (BŠ stands for the Bhatia-Šemrl property)

★ To find (norm-attaining) operators which belong to the subset BŠ(X,Y) and then study its denseness

The same question can be done for its complement. (BŠ stands for the Bhatia-Šemrl property)

★ To find (norm-attaining) operators which belong to the subset BŠ(X,Y) and then study its denseness

The same question can be done for its complement. (BŠ stands for the Bhatia-Šemrl property)

★ OH for homogeneous polynomials

★ NA(J), where J stands for the James space

**not** known that when (X,Y) satisfies the BPBp by assuming that X has the Radon-Nikodým property nor what happens with the particular case of James’ space J (this question was to me by ARZ)

★ Does the BPBp imply the BPBp for finite rank operators?

This question was made by RM to me

★ Non-norm-attaining tensors + lineability

ARZ already has some results (only one!) in this direction and maybe we could push it further

★ To study integral operators and when do they attain their norms

★ Set points of discontinuity of hyperplanarly continuous maps on Banach spaces

★ To study integral operators and when do they attain their norms

Dani sugiere que miremos lo siguientes artículos:

✩ *A continuous tale on continuous and separatey continuous functions*

✩ *On sets of discontinuous of functions continuous on all lines* by Zajicek

10. Counterexample for the density of the symmetric tensors

**S.D.**, Mingu

9. NA adjoint operators

**S.D.**, Miguel, Mingu (Notes)

“Perhaps the adjoint of every operator from \ell_1 into \ell_1 is norm-attaining”

8. NRA(X) contains no 2 dimensional Banach spaces

**S.D.**, Dani, Juan, Ella and Martina

7. Elements of tensor product space attaining their Chevet-Saphar norms

**S.D.**, Mingu

**S.D.**, Petr

5. Properties A, B, \alpha, \beta, quasi-\alpha, quasi-\beta for tensor products

**S.D.**, Mingu, Jaagup, LC and Abe

4. Funciones ES en espacios de sucesiones y funciones

**S.D.**, Dani, Juanito

3. Daugavet points in the homogenous polynomials spaces

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

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

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

Lineability

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?*

Norm-attaining theory

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