Mappings of Stable Cylindrical Measures in Banach Space

On the relationship between ? p -Radonifying operators and other operator ideals in Banach spaces of stable typep

“…These results extend the works of [5,10,20], and give the solutions to problems of [5]. We investigate the relationship between yp-Radonifying operators from Lv,(fLit) into E and other well-known operator ideals.…”

“…(1) ~ (2). Conversely, if T~ Np(X', E), then T is clearlyp-summing, and hence it is ?p-Radonifying by [20,Theorem 10] since E is of stable type p and of Sp type. Since E' is isomorphic to a complemented subspace ofLp,, by [2, Corollary 2], Tisp-integral, and hence it is p-nuclear (see [15,Corollary 1 ]).…”

“…The relations of Zp(Lp,, E) and Flp(Lp,, E) were studied by Chobanjan and Tarieladze [1], Linde et al [4,5], Mandrekar and Weron [10] and Thang and Tien [20]. The relations of Zp(Lp,, E) and Flp(Lp,, E) were studied by Chobanjan and Tarieladze [1], Linde et al [4,5], Mandrekar and Weron [10] and Thang and Tien [20].…”

On some properties of $\gamma_{p}$-summing operators in Banach spaces

“…We shall show that this result remains true without any additional assumption on F Remark that this result is false in the case r=p . If E is of stable type p , then it follows easily \Pi_{\gamma\rho}(G, E)=\Pi_{p}(G, E) for every Banach space G , as remarked by Thang and Tien [23]. We shall prove the converse: E is of stable type p , 1<p<2, if and only if for each (one infinite dimensional) space L_{p}', \Pi_{\gamma\rho}(L_{p}', E)=\Pi_{p}(L_{p}' , E) .…”

“…Denote by \Pi_{p}(E, F) the set of all p -summing operators from E into F . In [23], Thang and Tien proved that if F dose not contain c_{0} , Then every r -summing operator T:E arrow F is \gamma_{p} -summing where 1<r<p<2. We shall show that this result remains true without any additional assumption on F Remark that this result is false in the case r=p .…”