Erratum to: On the James type constant of l p − l 1
نویسندگان
چکیده
منابع مشابه
Commutators on L p , 1 ≤ p < ∞ †
The operators on Lp = Lp[0, 1], 1 ≤ p < ∞, which are not commutators are those of the form λI + S where λ , 0 and S belongs to the largest ideal in L(Lp). The proof involves new structural results for operators on Lp which are of independent interest.
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We prove that there is no sparse hard set for P under logspace computable bounded truth-table reductions unless P = L. In case of reductions computable in NC 1 , the collapse goes down to P = NC 1. We generalize this result by parameterizing the sparseness condition, the space bound and the number of queries of the reduction, apply the proof technique to NL and L, and extend all these theorems ...
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Let 1 < p ̸= 2 < ∞, ε > 0 and let T : lp(l2) into → Lp[0, 1] be an isomorphism Then there is a subspace Y ⊂ lp(l2), (1 + ε)-isomorphic to lp(l2), such that: T|Y is an (1+ ε)-isomorphism and T (Y ) is Kp-complemented in Lp [0, 1], with Kp depending only on p. Moreover, Kp ≤ (1 + ε)γp if p > 2 and Kp ≤ (1 + ε)γp/(p−1) if 1 < p < 2, where γr is the Lr norm of a standard Gaussian variable.
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Recently Takahashi has introduced James type constant. In this paper, we will introduce some new properties of the constant such as monotonicity, uniform non-squareness characterized by James type constant, and so on. We also investigate some relations between James type constant and other constants. Our main results of the paper are three examples of the constant. These examples include lp (p ...
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In a first course in functional analysis, a great deal of time is spent with Banach spaces, especially the interaction between such spaces and their dual spaces. Banach spaces are a special type of topological vector space, and there are important topological vector spaces which do not lie in the Banach category, such as the Schwartz spaces. The most fundamental theorem about Banach spaces is t...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2015
ISSN: 1029-242X
DOI: 10.1186/s13660-015-0663-y