Frames for Banach Spaces
| العنوان بلغة أخرى: |
الإطارات لـ فضاءات بناخ |
|---|---|
| المؤلف الرئيسي: | دلول، مرفت نافذ سعيد (مؤلف) |
| مؤلفين آخرين: | صرصور، جاسر حسن (مشرف) |
| التاريخ الميلادي: |
2017
|
| موقع: | غزة |
| الصفحات: | 1 - 105 |
| رقم MD: | 875330 |
| نوع المحتوى: | رسائل جامعية |
| اللغة: | الإنجليزية |
| الدرجة العلمية: | رسالة ماجستير |
| الجامعة: | الجامعة الإسلامية (غزة) |
| الكلية: | كلية العلوم |
| الدولة: | فلسطين |
| قواعد المعلومات: | Dissertations |
| مواضيع: | |
| رابط المحتوى: |
| المستخلص: |
In this thesis, we study frames in Hilbert and Banach spaces with their properties. We give three natural formulations for the notation of a frame of a Banach space. Then, we show that all three definitions give the same frames. Also, we show that these definitions are related to some forms of the approximation property. We also consider Hilbert space frames. Here we classify the alternate dual frames for a Hilbert space frame by a natural manifold of operators on the Hilbert space. Finally, we study a notion of a minimal associated sequence space and a minimal associated reconstruction operator for Schauder frames. We prove that a Schauder frame is a near Schauder basis if and only if the kernel of the minimal associated reconstruction operator contains no copy of C. In particular, we show that a Schauder frame for a Banach space with no copy of C. is a near Schauder basis if and only if minimal associated sequence space contains no copy of C.. In these cases, the a minimal associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the Schauder frame. |
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عناصر مشابهة
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