مشبکه های باناخ گروتندیک و کلاسهایی از عملگرهای −𝒑 همگرا

نویسندگان
حلیمه اردکانی
منیژه سلیمی
چکیده
مفهوم مجموعه های −𝐿 محدود از مرتبهی 𝑝 (1≤𝑝≤∞) در دوگان فضاهای باناخ و همچنین عملگرهای −𝑝 همگرا قبلا معرفی شدهاند. در این مقاله، نتایجی در مورد مجموعه های تقریباً −𝐿 محدود از مرتبهی 𝑝 در دوگان مشبکه های باناخ و عملگرهای −𝑝 همگرای مجزا به دست می آید. به ویژه، نتیجه میگیریم که مشبکه های باناخ با این ویژگی که هر مجموعهی −𝐿 محدود ) یا −𝐿 محدود از مرتبهی 𝑝 ) در دوگان آنها یک مجموعهی فشرده ضعیف نسبی باشد، دقیقاً همان فضاهای گروتندیک هستند. به علاوه، ثابت می شود که یک مشبکه باناخ 𝑀 از فضاهای عملگری خاصیت −𝑝 شور محدود مجزا دارد اگر و تنها اگر همه عملگرهای محاسبهای روی 𝑀 مجزای −𝑝 همگرا باشند.
کلیدواژه‌ها
−𝐿 مجموعه
دنباله ی –𝑝 جمعپذیر
عملگر –𝑝 همگرا
خاصیت –𝑝 شور
مشبکه ی باناخ

عنوان مقاله English

Grothendieck Banach lattices and classes of 𝒑− convergent operators

نویسندگان English

Halimeh Ardakani
Manijeh Salimi
چکیده English

Recently, the concept of 𝐿−limited subsets of order 𝑝 (1≤𝑝<∞) in dual Banach spaces and limited p-convergent operators are introduced. The paper is devoted to some results of almost 𝐿−limited subsets of order p in dual Banach lattices and disjoint limited 𝑝−convergent operators. In particular, we derive the following result: Banach lattices with the property that 𝐿−limited subsets (or 𝐿−limited subsets of order 𝑝) in their dual are relatively weakly compact, are precisely the Grothendieck spaces. Moreover, it is established that a Banach lattice 𝑀 of some operator spaces has the disjoint limited 𝑝−Schur property if and only if all evaluation operators on 𝑀 is disjoint limited p-convergent.

کلیدواژه‌ها English

L-set
weakly p-summable sequence
p-convergent operator
p-Schur property
Banach lattice
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