By Vesely L.
Given a Banach spaceX, letc 0(X) be the distance of all null sequences inX (equipped with the supremum norm). We convey that: 1) each one compact set inc 0(X) admits a (Chebyshev) middle iff each one compact set inX admits a middle; 2) forX fulfilling a definite situation (Q), each one bounded set inc 0(X) admits a middle iffX is quasi uniformly rotund. We build a Banach spaceX such that the compact subsets ofX admit centers,X satisfies the situation (Q) andX isn't really quasi uniformly rotund. It follows that the Banach spaceE=c 0(X) has the valuables from the name.
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Extra resources for A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers
157,405. J. A. Y. Chen (1983) Nucleic Acid Res. 11,7911. W. S. H. Doi (1984) Natl. Acad. Sei. USA 81,1184. -F. -L. -S. H. Doi 1 Department of Biochemistry and Biophysics, University of California Davis, California, 95616 I. , 1987). Although the exact mechanism of gene stimulation is not known, there appears to be a family of genes whose products can enhance transcriptional activity and may be transcriptional factors. Although studies to date have shown that mutations in these genes have a profound effect on the expression of extracellular protein genes, their effects on genes encoding intracellular proteins is less understood.
Natto sen gene. The DNA sequence of the coding strand is given from 5' to 3', numbered from nucleotide 1 at the EcoRV site. The deduced amino acid sequence is given below the DNA sequence with the Nterminal methionine as residue number 1. Locations of important restriction site are shown above the DNA sequence. 6 kcal/mol) are underlined. defining it as a new gene different from all other known genes with similar phenotype, including sacQ, sacU, prtR, and hpr. When the sen gene is present in high copy number, it stimulates the expression of both alkaline and neutral proteases by 3 - 4 fold.
We examined the decay rate of the aprE mRNA by estimating the intensity of the 520 bp bands. , 1987), indicating that prtR does not affect mRNA stability. IV. CONCLUSIONS We isolated a protein whose amino acid composition and aminoterminal amino acid sequence were those expected from the DNA sequence of prtR. It was found that prtR enhanced mRNA level of the aprE gene and that this enhancement was not due to stabilization of mRNA. The possible involvement of prtR action at the translation and secretion steps was ruled out.
A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers by Vesely L.