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1
Summable Series and Convergence Factors
Convergence factor theorems for convergence factors of type I, in series
summable by Cesaro means, 45, 46. double series summable by Cesaro means,
57, 59. — — — — — k — — — —— n-tuple series summable by Cesare means,
76, 77.
Charles Napoleon Moore, 1938
2
Topological Vector Spaces
(ii) A family {xx: a e A} c £ is summable to x e E if for each 0- neighborhood U in E,
there exists a finite subset A, c A such that for each finite set i1> satisfying 0>v c it
> c A, it is true that X xxex + U. x E <X> This is expressed by writing x = Xxxx .If ...
H.H. Schaefer, Manfred P. H. Wolff, 1999
3
The Elements of Operator Theory
It is called a p-summable family for some p > 1 if {| a summable family of positive
numbers. In particular, {x7}7£ p is an absolutely summable family if {H^H^er is a
summable family, and a square- summable family if {H^P^er is a summable ...
4
Introduction to Tensor Products of Banach Spaces
A sequence (xn) in a Banach space is said to be summable if the series 5Zn xn
converges, or, in other words, the partial sums E'% xi form a Cauchy sequence.
The sequence (a;,,) is absolutely summable if the series Yln \\xn\\ converges.
5
Absolutely Summing Operators
UNCONDITIONAL AND ABSOLUTE SUMMABILITY IN BANACH SPACES THE
DVORETZKY- ROGERS THEOREM Recall that a sequence (xn) in a normed
space is absolutely summable if £^n ||xn|| < oo, and is unconditionally summable
if ...
6
Calculus and Analysis: A Combined Approach
In the following, we define and study absolutely summable sequences. Any
reordering of such a sequence leads to a convergent series whose sum
coincides with the sum of the original series. In applications mainly absolutely
summable ...
7
Advanced Calculus: An Introduction to Modern Analysis
8. Show that if/ is a measurable function on an interval / and if |/| < g a.e., where 0
is a summable function on /, then / is summable on J. 9. Show that if/is a
measurable function on a finite interval / and if |/| < M a.e., then/is summable over
/. 10.
A normed vector space X is complete if and only if every absolutely summable
series in X is summable. That is, X is complete if and only if X^li xn converges in
X whenever J^Li \\xn\\ < oo. PROOF. First suppose that A" is complete, and let (xn
) ...
9
General Topology: Chapters 1-4
summable for all t, but that the (countable) set of indices , such that *, =;£ o
depends on t. For this reason we shall not impose any hypothesis on the power
of the index set in what follows. 1. FAMILIES OF POSITIVE FINITE NUMBERS ...
10
Convergence Analysis of Proximal-like Methods for ...
44 Choice of Q in the summable-error-framework (Kullback-Leibler) . . . . . . 181
Choice of X0 in the summable-error-framework (Kullback-Leibler) . . . . . 181
Choice of 'ymaX in the summable-error-framework (Kullback-Leibler) . . . . 182
Choice ...
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Why a Libertarian Might Not Be Thrilled with the Resolution of the …
But I have a sneaking sense that pre-Enlightenment attitudes roughly summable as "error has no rights" (it's just what the tribe thinks of as error that changes) ... «Reason, 三月 15»
With Japan-China Political Relations Still Frozen, Japan Business …
China's leaders universally acknowledge that economic, trade, and investment relations with Japan–summable in the word and in the form of “technology”–have ... «Forbes, 九月 14»
Bands Won't Play No More
They want moments to sum up the un-summable. In the wake of 9/11, good records with a lashing of dread or bravado, like Bob Dylan's Love and Theft, could ... «Pitchfork Media, 八月 11»
Bilgisayar sözlüğü ve internet acil çantası
absolutely stable system : mutlak kararlı dizge ? absolutely summable : mutlak toplanır? absorb, to : soğurmak(nesne ya da gazı emmek) ? absorbant : soğurgan ... «Milliyet, 八月 09»
