Strictly singular operators and isomorphisms of Cartesian products of power series spaces

V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind E0p(a)×E¥ q(b) where 1 £ p,q £ ¥, p ¹ q, a = (an)n=1¥ and b = (bn)n=1¥ are sequences of positive numbers and E0p(a), E¥ q (b) are respectively lp-finite and lq-infinite type power series spaces

Factorization of unbounded operators on Köthe spaces

The main result is that the existence of an unbounded continuous linear operator T between Kothe spaces lambda(A) and lambda(C) which factors through a third Kothe space A(B) causes the existence of an unbounded continuous quasidiagonal operator from lambda(A) into lambda(C) factoring through lambda(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (lambda(A), lambda(B)) is an element of B (which means that all continuous linear operators from lambda(A) to lambda(B) are bounded). The proof is based on the results of [9) where the bounded factorization property BF is characterized in the spirit of Vogt's [10] characterization of B. As an application, it is shown that the existence of an unbounded factorized operator for a triple of Kothe spaces, under some additonal asumptions, causes the existence of a common basic subspace at least for two of the spaces (this is a factorized analogue of the results for pairs [8, 2])

Alterations of store-operated calcium entry and cyclopiazonic acid-induced endothelium-derived relaxations in aging rat thoracic aorta

The purpose of our study was to investigate whether endothelium-derived relaxations induced by store depletion are altered in aging rat thoracic aorta. Vascular responses were measured in aortic segments isolated from young (2–4 month) and old (20–24 month) male Sprague-Dawley rats. In phenylephrine-contracted intact tissues, receptor-mediated and receptor-independent endothelium-derived relaxations were induced by acetylcholine (ACh) and sarcoplasmic/endoplasmic reticulum Ca2+ ATPase (SERCA) blocker cyclopiazonic acid (CPA), respectively. In addition, CPA-induced changes in intracellular calcium levels were monitored in fura-2-loaded endothelium-denuded tissues. Real-time quantitative reverse transcription polymerase chain reaction and western blot analysis were performed to determine the transient receptor potential canonical (TRPC) 4 mRNA and protein levels. Endothelial TRPC4 mRNA levels were apparently decreased in aging rats. Immunoblot analysis showed that TRPC4 protein levels significantly decreased in intact aorta from 20- to 24-month-old rats compared to that from 2- to 4-month-old rats. ACh- and CPA-induced endothelium-dependent relaxations decreased in old rat aorta without any change in direct vasodilation induced by sodium nitroprusside. Store-operated Ca2+ entry (SOCE) induced by CPA was significantly decreased, whereas sarcoplasmic reticulum Ca2+ release was unaffected in endothelium-denuded aging rat aorta. In conclusion, TRPC4 downregulation could be associated with decreased endothelium-dependent vasorelaxations. As endothelial nitric oxide synthase is activated by SOCE-induced caveolar internalization, tracking the expression levels of SERCA, ion channels, and/or associated proteins involved in SOCE would lead to the development of novel therapeutics for age-related vasospastic disorders with dysfunctional endothelium

Generalized Timelike Mannheim Curves in Minkowski space-time E14E_1^4

We give a definition of generalized timelike Mannheim curve in Minkowski space-time $E_1^4$. The necessary and sufficient conditions for the generalized timelike Mannheim curve obtain. We show some characterizations of generalized Mannheim curve