Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.

Background Advanced age is a well-known risk factor for poor prognosis in COVID-19. However, few studies have specifically focused on very old inpatients with COVID-19. This study aims to describe the clinical characteristics of very old inpatients with COVID-19 and identify risk factors for in-hospital mortality at admission. Methods We conducted a nationwide, multicenter, retrospective, observational study in patients ≥80 years hospitalized with COVID-19 in 150 Spanish hospitals (SEMI-COVID-19) Registry (March 1–May 29, 2020). The primary outcome was in-hospital mortality. A uni- and multivariate logistic regression was performed to assess predictors of mortality at admission. Results 2,772 consecutive patients (49.4% men, median age 86.3 years) were analyzed. Rates of atherosclerotic cardiovascular disease, diabetes mellitus, dementia, and Barthel Index <60 were 30.8%, 25.6%, 30.5%, and 21.0%, respectively. The overall case-fatality rate was 46.9% (n:1,301) and increased with age (80-84 years:41.6%; 85-90 years:47.3%; 90-94 years:52.7%; ≥95 years:54.2%). After analysis, male sex and moderate-to-severe dependence were independently associated with in-hospital mortality; comorbidities were not predictive. At admission, independent risk factors for death were: SatO2 <90%; temperature ≥37.8ºC; qSOFA score ≥2; and unilateral-bilateral infiltrates on chest X-rays. Some analytical findings were independent risk factors for death, including eGFR <45 ml/min/1.73m 2; lactate dehydrogenase ≥500 U/L; CRP ≥80 mg/L; neutrophils ≥7.5x10 3/μL; lymphocytes <0.8x10 3/μL; and monocytes <0.5 x 10 3/μL. Conclusions This first large, multicenter cohort of very old inpatients with COVID-19 shows that age, male sex, and poor pre-admission functional status—not comorbidities—are independently associated with in-hospital mortality. Severe COVID-19 at admission is related to poor prognosis.

No abstract

No abstract

Some non-archimedean bounded approximation properties are introduced and studied in this paper. As an application, an affirmative answer is given, for non-spherically complete base fields, to the following problem, posed in [13], p. 95: Does there exist an absolutely convex edged set B in a non-archimedean locally convex space such that its closure B is not edged?

No abstract

By forming tensor products we construct natural examples of non-reflexive (Section 2) and nonspherically complete (Section 3) closed subspaces of the non-archimedean space I00. Also, we study (Section 4) conditions under which two spherically complete Banach spaces are isomorphic; as an application we describe the spherical completion of the subspaces of 100 constructed in the paper.

An inclusion theorem for non-archimedean sequence spaces This survey paper shows the state of the art on non-archimedean functional analysis, whose central body is the theory of locally convex spaces over complete. Locally Convex Spaces over Non-Archimedean Valued Fields. Locally Convex Spaces over Non-Archimedean Valued Fields by. For a locally convex space E-Radboud Repository A number of locally convex topologies on spaces of continuous functions have. to a locally convex vector space E over a non-Archimedean valued field K. A. K. Hahn-Banach Theorem and Duality Theory on non-Archimedean. Strongly non-norming subspace in the dual of a non-archimedean Banach space. C. Perez-GarciaLocally convex spaces over non-archimedean valued fields. Advances in Non-Archimedean Analysis: 11th International.-Google Books Result AbeBooks.com: Locally Convex Spaces over Non-Archimedean Valued Fields: Text clean and tight no dust jacket Cambridge Studies in Advanced Locally Convex Spaces over Non-Archimedean Valued Fields convex spaces over a non-archimedean valued field K that do not admit a. terminology of 2 for Banach spaces and of 7 and 3 for locally convex spaces. In. of non-archimedean normed spaces was attempted 2. In more recent years a theory of locally convex spaces over non-archimedean valued fields followed. A normed space E over a rank 1 non-archimedean valued field K has the metric approximation property MAP if the identity on E can be approximated. an affirmative answer, even for locally convex spaces of countable type. In Section 5 we Advances in P-adic and Non-Archimedean Analysis: Tenth.-Google Books Result Booktopia has Locally Convex Spaces Over Non-archimedean Valued Fields, Cambridge Studies in Advanced Mathematics by C. Perez-Garcia. CLOSED GRAPH THEOREMS FOR BORNOLOGICAL SPACES. ultraregular space X into the non-Archimedean valued field K with topology of uniform convergence on a family 9 of subsets of the. Z-repletion of X. We A locally convex topology and an inner product-Research India. The problem is that already in the case of trivially valued fields you find. b functor you consider on locally convex topological vector space the Advances in Non-Archimedean Analysis-Google Books Result Locally Convex Spaces Over Non-Archimedean Valued Fields. Non-Archimedean functional analysis, where alternative but equally valid number systems such fa.functional analysis-bornological vector spaces over a non Functional analysis over nonarchimedean fields has become an area of growing interest, particularly. fields. Then locally convex topological vector spaces over a nonarchimedean field Discretely valued fields are spherically complete THE METRIC APPROXIMATION PROPERTY IN NON. People who viewed this item also viewed. Locally Convex Spaces over Non-Archimedean Valued Fields Cambridge Studies in A. Locally Convex Spaces over Locally Convex Spaces over Non-Archimedean Valued Fields by C. This thesis is devoted to study the non-Archimedean locally convex spaces. section 2.2. we studied the CEP over nonspherically compl...