Wyniki wyszukiwania - Biblioteka Nauki

1

$ℒ_p$-Spaces and injective locally convex spaces

100%

Domański P.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction.................................................................................................................................................................5 Conventions and notations.........................................................................................................................................8 1. Preliminaries from the theory of locally convex spaces.........................................................................................11 2. Ultraproducts of locally convex spaces.................................................................................................................16 3. The principle of local reflexivity for locally convex spaces.....................................................................................19 4. Complemented subspaces of products and direct sums of Banach $L_p$-spaces and L₁ -predual spaces........24 5. Definition, examples and basic properties of locally convex $ℒ_p$-spaces..........................................................29 6. Definition, examples and basic properties of $Dℒ_p$-spaces..............................................................................39 7. Local properties of complemented subspaces of products and direct sums of Banach $L_p$-spaces................42 8. Duality between $ℒ_p$ and $Dℒ_p$-spaces and a characterization of injective spaces.....................................46 9. Extension, lifting and factorization properties of $ℒ_p$ and $Dℒ_p$-spaces.......................................................56 10. Fréchet $ℒ_p$- and (DF)-&Dℒ_p$-spaces with applications to Fréchet injective spaces..................................62 11. Comments and open problems...........................................................................................................................71 References...............................................................................................................................................................73

2

Algebra of multipliers on the space of real analytic functions of one variable

58%

Domański P. , Langenbruch M.

Studia Mathematica

|

2012

|

tom 212

|

nr 2

155-171

EN

We consider the topological algebra of (Taylor) multipliers on spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We describe multiplicative functionals and algebra homomorphisms on that algebra as well as idempotents in it. We show that it is never a Q-algebra and never locally m-convex. In particular, we show that Taylor multiplier sequences cease to be so after most permutations.

3

Köthe coechelon spaces as locally convex algebras

58%

Bonet J. , Domański P.

|

tom 199

|

nr 3

241-265

EN

We study those Köthe coechelon sequence spaces $k_{p}(V)$, 1 ≤ p ≤ ∞ or p = 0, which are locally convex (Riesz) algebras for pointwise multiplication. We characterize in terms of the matrix V = (vₙ)ₙ when an algebra $k_{p}(V)$ is unital, locally m-convex, a 𝒬-algebra, has a continuous (quasi)-inverse, all entire functions act on it or some transcendental entire functions act on it. It is proved that all multiplicative functionals are continuous and a precise description of all regular and all degenerate maximal ideals is given even for arbitrary solid algebras of sequences with pointwise multiplication. In particular, it is shown that all regular maximal ideals are solid.

4

Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions

58%

Domański P. , Lindström M.

|

2002

|

tom 79

|

nr 3

233-264

EN

We give an elementary approach which allows us to evaluate Seip's conditions characterizing interpolating and sampling sequences in weighted Bergman spaces of infinite order for a wide class of weights depending on the distance to the boundary of the domain. Our results also give some information on cases not covered by Seip's theory. Moreover, we obtain new criteria for weights to be essential.

5

The space of real-analytic functions has no basis

58%

Domański P. , Vogt D.

Studia Mathematica

|

2000

|

tom 142

|

nr 2

187-200

EN

Let Ω be an open connected subset of $ℝ^d$. We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.

6

The current state of knowledge on small cell and non-small cell lung cancer and the position of durvalumab immunotherapy in lung cancer treatment

47%

Poboży K. , Domańska J. , Domański P.

OncoReview

|

2022

|

tom 12

|

nr 4

75-82

EN

Lung cancer is the second most frequently diagnosed cancer and the leading cause of cancer-related deaths in the world. These statistics make lung cancer one of the most important targets for modern medicine. The identification of multiple risk factors, including tobacco smoking, has been fundamental in understanding the disease. Late-stage detection is a significant contributor to the high mortality rate of lung cancer. Nonetheless, the role of screening is still debatable. The selection of therapy is primarily based on distinguishing between small-cell and non-small cell lung cancer. Despite the major differences in treatment, in both types in specific situations the treatment involves durvalumab – a monoclonal antibody targeting the programmed cell death ligand 1 molecule, which is often present on tumor cells and protects them against the patient’s immune system. The efficacy of durvalumab has been demonstrated in two randomized, multicenter clinical trials. The aim of this study is to summarize the current state of knowledge about lung cancer and durvalumab. Despite the current 5-year survival rate of 19% in lung cancer, the development of immunotherapeutics such as durvalumab may be the key to improving the unfavorable prognosis of lung cancer in the future.

7

Neoantigen therapeutic cancer vaccines: a promising approach to personalized immunotherapy

47%

Poboży K. , Domańska J. , Domański P.

OncoReview

|

2023

|

tom 13

|

nr 4

93-98

EN

The tumour microenvironment diversity among patients poses a challenge for conventional therapies, leading to limited efficacy. Furthermore, conventional methods are inherently associated with a negative impact on healthy tissues. Personalized immunotherapy, focused on individual tumor characteristics, has emerged as a potential solution. Neoantigens, unique antigens arising from tumour-specific mutations, play a crucial role in personalized therapy. Identifying and utilizing neoantigens through therapeutic vaccines can induce an immune response specifically against tumour cells, offering a more targeted and less toxic for healthy tissues approach to cancer treatment. The vaccines can potentially lead to tumour regression and improved outcomes. The effectiveness of this therapy is still limited due to phenomena such as immune escape. However, ongoing scientific research, technological advancements, and emerging combination therapies offer hope for the success of neoantigen-based therapeutic cancer vaccines, ushering in a new era in personalized oncology.

8

Poly(adP-ribose) polymerase inhibitor olaparib in the treatment of ovarian cancer: a comprehensive review of current literature

47%

Poboży K. , Domańska J. , Domański P.

OncoReview

|

2023

|

tom 13

|

nr 2

39-47

EN

Purpose of the review: This comprehensive review aims to provide a summary of current research on the utilization of olaparib, a poly(ADP-ribose) polymerase (PArP) inhibitor, in the treatment of ovarian cancer. The review aims to highlight the key findings from recent clinical trials and assess the potential of olaparib as a targeted therapy for improving the prognosis of ovarian cancer patients. recent findings: Ovarian cancer remains a significant global health concern with high mortality rates. While optimal debulking surgery and platinum-based chemotherapy are the standard treatments, the recurrence rates remain substantial. The emergence of PArP inhibitors, particularly olaparib, has intro duced a novel therapeutic approach that targets the genomic instability and DnA repair mechanisms in cancer cells. notable clinical trials, such as SOl O1, SOl O2, and PAOlA-1, have demonstrated the effectiveness of olaparib in significantly improving progression-free survival, particularly in patients with Br CA mutations or homologous recombination deficiency. Additionally, combination therapies involving olaparib, such as those with bevacizumab or entinostat, have shown promising results. Summary: The utilization of olaparib has brought about a paradigm shift in the treatment of ovarian cancer. notably, it has shown significant improvements in progression-free survival and overall survival, particularly in patients with Br CA mutations or homologous recombination deficiency. The exploration of olaparib through various clinical trials and combination therapies continues to provide valuable insights and offer new prospects for ovarian cancer patients. Moreover, the growing understanding of PArP inhibitors holds the potential for further advancements in the prognosis of patients with this formidable condition.

9

Uncomplementability of the spaces of norm continuous functions in some spaces of "weakly" continuous functions

47%

Domański P. , Drewnowski L.

|

nr 3

245-251

10

Advances in immunotherapy for osteosarcoma: a review of emerging treatment strategies

41%

Poboży K. , Domański P. , Domańska J. , Konarski W. , Poboży T.

OncoReview

|

2023

|

tom 13

|

nr 3

75-84

EN

Advances in immunotherapy for osteosarcoma have shown promising results, with the use of monoclonal antibodies and immune checkpoint inhibitors. These strategies are aimed at targeting specific molecules and pathways involved in tumour immune evasion and promoting anti-tumour immune responses. Other emerging immunotherapeutic approaches include autophagy and pyroptosis induction, chimeric antigen receptor T-cell therapy, gadolinium-bisphosphonate nanoparticles and dendritic cell-based vaccines. Continued research into these emerging treatment strategies is essential for developing effective therapies for patients with high-grade osteosarcoma.