Displaying similar documents to “Functions of the form ∑ i = 1 N f i ( x ) g i ( t ) in L 2 ”

On some geometric properties of certain Köthe sequence spaces

Yunan Cui, Henryk Hudzik, Tao Zhang (1999)

Mathematica Bohemica

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It is proved that if a Kothe sequence space X is monotone complete and has the weakly convergent sequence coefficient WCS ( X ) > 1 , then X is order continuous. It is shown that a weakly sequentially complete Kothe sequence space X is compactly locally uniformly rotund if and only if the norm in X is equi-absolutely continuous. The dual of the product space ( ⨁ i = 1 ∞ X i ) Φ of a sequence of Banach spaces ( X i ) i = 1 ∞ , which is built by using an Orlicz function Φ satisfying the Δ 2 -condition, is computed isometrically (i.e....

On the divisibility of power LCM matrices by power GCD matrices

Jian Rong Zhao, Shaofang Hong, Qunying Liao, Kar-Ping Shum (2007)

Czechoslovak Mathematical Journal

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Let S = { x 1 , ⋯ , x n } be a set of n distinct positive integers and e ≥ 1 an integer. Denote the n × n power GCD (resp. power LCM) matrix on S having the e -th power of the greatest common divisor ( x i , x j ) (resp. the e -th power of the least common multiple [ x i , x j ] ) as the ( i , j ) -entry of the matrix by ( ( x i , x j ) e ) (resp. ( [ x i , x j ] e ) ) . We call the set S an odd gcd closed (resp. odd lcm closed) set if every element in S is an odd number and ( x i , x j ) ∈ S (resp. [ x i , x j ] ∈ S ) for all 1 ≤ i , j ≤ n . In studying the divisibility of the power LCM and power GCD matrices, Hong conjectured in...