# 2-summing multiplication operators

Studia Mathematica (2013)

- Volume: 216, Issue: 1, page 77-96
- ISSN: 0039-3223

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topDumitru Popa. "2-summing multiplication operators." Studia Mathematica 216.1 (2013): 77-96. <http://eudml.org/doc/285383>.

@article{DumitruPopa2013,

abstract = {Let 1 ≤ p < ∞, $ = (Xₙ)_\{n∈ℕ\}$ be a sequence of Banach spaces and $l_\{p\}()$ the coresponding vector valued sequence space. Let $ = (Xₙ)_\{n∈ℕ\}$, $ = (Yₙ)_\{n∈ℕ\}$ be two sequences of Banach spaces, $ = (Vₙ)_\{n∈ℕ\}$, Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator $M_\{\}: l_\{p\}() → l_\{q\}()$ by $M_\{\}((xₙ)_\{n∈ℕ\}) : = (Vₙ(xₙ))_\{n∈ℕ\}$. We give necessary and sufficient conditions for $M_\{\}$ to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞.},

author = {Dumitru Popa},

journal = {Studia Mathematica},

keywords = {-summing; nuclear operators; operator ideals},

language = {eng},

number = {1},

pages = {77-96},

title = {2-summing multiplication operators},

url = {http://eudml.org/doc/285383},

volume = {216},

year = {2013},

}

TY - JOUR

AU - Dumitru Popa

TI - 2-summing multiplication operators

JO - Studia Mathematica

PY - 2013

VL - 216

IS - 1

SP - 77

EP - 96

AB - Let 1 ≤ p < ∞, $ = (Xₙ)_{n∈ℕ}$ be a sequence of Banach spaces and $l_{p}()$ the coresponding vector valued sequence space. Let $ = (Xₙ)_{n∈ℕ}$, $ = (Yₙ)_{n∈ℕ}$ be two sequences of Banach spaces, $ = (Vₙ)_{n∈ℕ}$, Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator $M_{}: l_{p}() → l_{q}()$ by $M_{}((xₙ)_{n∈ℕ}) : = (Vₙ(xₙ))_{n∈ℕ}$. We give necessary and sufficient conditions for $M_{}$ to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞.

LA - eng

KW - -summing; nuclear operators; operator ideals

UR - http://eudml.org/doc/285383

ER -

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