The Strong Property (B) for $$L_p$$ Spaces

Given a purely non-atomic, finite measure space $$(\Omega ,\Sigma ,\nu )$$ ( Ω , Σ , ν ) , it is proved that for every closed, infinite-dimensional subspace V of $$L_p(\nu )$$ L p ( ν ) ($$1\le p<\infty $$ 1 ≤ p < ∞ ) there exists a decomposition $$L_p(\nu )=X_1\oplus X_2$$ L p ( ν ) = X 1 ⊕ X 2 , such that both subspaces $$X_1$$ X 1 and $$X_2$$ X 2 are isomorphic to $$L_p(\nu )$$ L p ( ν ) and both $$V\cap X_1$$ V ∩ X 1 and $$V\cap X_2$$ V ∩ X 2 are infinite-dimensional. Some consequences concerning dense, non-closed range operators on $$L_1$$ L 1 are derived.

NEW RESULTS ON SEMICLOSED LINEAR RELATIONS

This paper has triple main objectives. The first objective is an analysis ofsome auxiliary results on closedness and boundednes of linear relations. The seconde objective is to provide some new characterization results on semiclosed linear relations. Here it is shown that the class of semiclosed linear relations is invariant under finite and countable sums, products, and limits. We obtain some fundamental new results as well as a Kato Rellich Theorem for semiclosed linear relations and essentially interesting generalizations. The last objective concern semiclosed linear relation with closed range, where we have particularly established new characterizations of closable linear relation.

Atom based Profiling and Functional Enrichment analysis of Aquaporins

Sequence analysis is a computational biology method to study protein sequences by comparing amino acids of one protein sequence with the other (residual level comparison). This study reveals a new concept of comparing protein sequences at their basic atomic level. Aquaporins from various origin were compared at their atomic level and the study revealed that all the aquaporin proteins have a closed range of 31.0% to 34.2% of carbon atoms irrespective of their origin and amino acid sequence. Further the protein interaction and functional enrichment analysis of AQP7 showed significant interaction with glycerol kinase and ATP-sensitive inward rectifier potassium channel protein. Our insilico analysis on aquaporin proteins exposed that nature tends to maintain the overall carbon atom composition in the proteins regardless of their amino acid sequence composition which could be further used for their classification. Also, the most highly interacting partners for AQPs are the potassium buffering channel proteins.

THE HAUSDORFF MOMENT PROBLEM IN THE LIGHT OF ILL-POSEDNESS OF TYPE I

The Hausdorf moment problem (HMP) over the unit interval in an L 2 -setting is a classical example of an ill-posed inverse problem. Since various applications can be rewritten in terms of the HMP, it has gathered significant attention in the literature. From the point of view of regularization it is of special interest because of the occurrence of a non-compact forward operator with non-closed range. Consequently, HMP constitutes one of few examples of a linear ill-posed problem of type I in the sense of Nashed. In this paper we highlight this property and its consequences, for example, the existence of an infinite-dimensional subspace of stability. On the other hand, we show conditional stability estimates for the HMP in Sobolev spaces that indicate severe ill-posedness for the full recovery of a function from its moments, because H ̈older-type stability can be excluded. However, the associated recovery of the function value at the rightmost point of the unit interval is stable of H ̈older-type in an H1 -setting. We moreover discuss stability estimates for the truncated HMP, where the forward operator becomes compact. Some numerical case studies illustrate the theoretical results and complete the paper.

Properties of multiplication operators on the space of functions of bounded φ-variation

In this paper, the functions u ∈ B V φ [ 0 , 1 ] u\in B{V}_{\varphi }\left[0,1] which define compact and Fredholm multiplication operators M u {M}_{u} acting on the space of functions of bounded φ \varphi -variation are studied. All the functions u ∈ B V φ [ 0 , 1 ] u\hspace{-0.08em}\in \hspace{-0.08em}B{V}_{\varphi }\left[0,\hspace{-0.08em}1] which define multiplication operators M u : B V φ [ 0 , 1 ] → B V φ [ 0 , 1 ] {M}_{u}:B{V}_{\varphi }\left[0,1]\to B{V}_{\varphi }\left[0,1] with closed range are characterized.

Closed range weighted composition operators between L^{p}-spaces

We characterize the closedness of ranges of weighted composition operators between \(L^p\)-spaces, where \(1 \leq p \leq \infty\). When the \(L^p\)-spaces are weighted sequence spaces, several corollaries about this class of operators are also deduced.