فضاهای تابعی و طولپایی ها فضاهای تابعی و طولپایی ها

توضیحات

مطالعۀ فضاهای تابعی (بر یک فضای توپولوژیک هاسدورف) و ارتباط بین ساختار جبری آنها و ساختار توپولوژیک فضای زمینه از مسایل با قدمت زیاد است. یکی از این ارتباط‌های مهم به‌وسیلۀ طولپایی‌های بیان می‌شود. به همین جهت مسیلۀ بررسی طولپایی‌ها (خطی یا غیرخطی) نسبت به نرم‌های مختلف، از موضوع‌های مهم در پژوهش‌های مختلف بوده است. , ,

متذکر می‌شویم که در مطالعۀ طولپایی‌ها، یا به طور کلی نگاشت‌های بین فضاهای تابعی که در ویژگی خاصی نسبت به نرم صدق می‌کنند، مرزها، به‌ویژه مرز شوکه و همچنین مجموعۀ نقاط قله یا قلۀ ضعیف و ارتباط آنها با یکدیگر، از اهمیت بسیاری برخوردار هستند. , ,دو هدف اصلی در نگارش این کتاب مد نظر بوده است. نخست اینکه ضمن بیان مقدمه مختصری از آنالیز تابعی و جبرهای (تابعی) باناخ، از آنجا که منابع محدودی در زمینۀ مرزها برای فضاهای تابعی (و حتی جبرهای تابعی در حالت موضعاً فشرده) وجود دارد، تلاش شده است که منبع مناسبی در زمینۀ نقاط فرین گوی یکۀ دوگان فضاهای تابعی، مرز شوکه، مرز شیلوف، نقاط مرزی قوی و ارتباط آنها با یکدیگر برای فضاهای تابعی بر یک فضای هاسدورف موضعاً فشرده، فراهم شود. دوم اینکه نتایج شناخته‌شده در رابطه با طولپایی‌های خطی بین فضاهای تابعی خاصی، نسبت به نرم سوپرمم و نرم‌های دیگر، و نیز بخشی از پژوهش‌های اخیر در رابطه با تعمیم‌های غیرخطی و همچنین ضربی این نتایج، ارایه شود. برای سهولت مطالعه سعی شده است مطالب تا حد امکان باز شده و با بیان ساده ارایه شود.,

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