F_n is weakly p-summable in c k x
Webp-weakly summable sequence (xn)inX, satisfying that the operator ( n) 2 lq! P nxn2Xis compact, lies in the range of anX-valued measure) with bounded variation. They are … Weboperator, and the spectral decomposition of T is given by en(x) = exp(2πnx), n∈ Z− 0, and λn = 1/(2πn). Proof of the theorem: Choose fn in Hof norm one with → αwhere ±α= T . By compactness we can assume fn converges to a limit f; then Tf= αf, and we may restrict to the subspace comple-mentary to fand continue.
F_n is weakly p-summable in c k x
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WebJan 1, 2003 · the form (x n) → h f n, x n i n for some sequence (f n) contained in the polar of some τ -neighbourhood of 0. W e shall characterise weakly- p -summable and N -n ull sequences in terms WebSome classes of p-summing type operators. OscarBlasco∗ and TeresaSignes† Abstract LetX,Y beBanachspacesanddenoteby w p(X,Y), sp(X,Y)and p(X,Y ...
Webthis linear space of X -valued sequences is a Banach space (if X is) when the ℓ pweak -norm. The sequence ( yn) in Y is the absolutely p -summable when. naturally, is just . … Webf. if and only if following holds. Weakly convergent definition (from Wikipedia): A sequence of points ( x n) in a Hilbert space H is said to converge weakly to a point x in H if x n, x …
WebMar 5, 2024 · Plenty of examples can be found in [24,25, 31, 62,63]; we mention just a few: for p ≥ 1, the class ℓ p (·) of absolutely p-summable sequences, the class ℓ w p (·) of weakly p-summable ... WebFeb 3, 2016 · A sequence $(x_n)$ is weakly $p$ summable if the mapping $e_n\mapsto x_n$ extends to a bounded linear operator from $\ell_{p^*}$ into $X$. IMO, this is the …
Webp-Cauchy sequence introduced by Chen et al. [6]. A sequence (xn)n in a Banach space Xis weakly p-Cauchy if for each pair of strictly increasing sequences (kn)n and (jn)n of positive integers, the sequence (xk n − xj n)n is weakly p-summable in X.Notice that, every weakly p-convergent sequence is weakly p-Cauchy, and the weakly ∞-Cauchy ...
Webp-operatorsummableifforeach f n ∈ lw ∗ p (X ∗)wehave s f n(x k) k n ∈ l p (l p).Everynorm p-summable sequence in a Banach space is operator p-summable whereas in its turn … small gingham black and white tableclothWebFeb 26, 2010 · A new type of convergence (called uniformly pointwise convergence) for a sequence of scalar valued functions is introduced. If (f n) is a uniformly bounded sequence of functions in l ∞ (Γ), it is proved that: (i) (f n) converges uniformly pointwise on Γ to some function f if, and only if, every subsequence of (f n) is Cesaro summable in l ... songs with brick in the titleWebsequences (kn)n and (jn)n of positive integers, the sequence (xk n − xj n)n is weakly p-summable in X[6]. Notice that, every weakly p-convergentsequence is weakly p-Cauchy, and the weakly ∞-Cauchy sequences are precisely the weakly Cauchy sequences. A bounded linear operator Tbetween two Banach spaces is called p-convergent, if it ... songs with bunch in the titleWebhxni is (norm) p-summable in X if P∞ n=1kxnk p < ∞. If P∞ n=1 f(xn) p < ∞, for all f ∈ X∗, then we say that hx ni is weakly p-summable in X. It is easy to note that a norm p … songs with burn in the titleWebLet X be p-summable relative to (F.G) Assume F is reflexive and IF.G is uniformly σ-additive Let K ⊂ L1F.G (B X) be a set satisfying the following conditions: (1) K is bounded in L1F.G (B X); (2) H1An → 0 in uniformly for H ∈ K, whenever An ∈ P and Then K is conditionally weakly compact in L 1F.G (B X). songs with bus in the title<\infty ; L (c_0,X)\simeq \ell _p^w (X) for p=1; T\rightarrow (T (e_n)) ( [ 16, 10, Proposition 2.2, p. 36]). Let 1\le p<\infty . songs with bury in the titleWebOct 23, 2024 · The weakly 1-summable sequences are precisely the weakly unconditionally convergent series. We recall the following isometries: L (\ell _ {p^*},X) \simeq \ell _p^w (X) for 1 songs with brother in the lyrics