کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9516886 | 1633121 | 2005 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Continuity of injective basis separating maps
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
We prove that certain (“basis separating”) linear injections are automatically continuous. We discuss openness of such maps in Section 5. There are two stages to the proof of continuity: (1) An injective basis separating map can be written in a canonical form (Theorem 4.3). (2) Any map of this form is continuous (Theorem 4.4). Given Banach spaces X and Y with Schauder bases {xn} and {yn}, respectively, we say that H:XâY, H(ânâNx(n)xn)=ânâNHx(n)yn, is basis separating if for all elements x=ânâNx(n)xn and y=ânâNy(n)xn of X, x(n)y(n)=0 for all nâN implies that Hx(n)Hy(n)=0 for all nâN. Associated with any linear basis separating map H, there is a support maph:NâNâ that we discuss in Section 3. The support map enables us to develop the canonical form (Eq. (3.2)) for basis separating maps.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 153, Issues 5â6, 1 December 2005, Pages 724-734
Journal: Topology and its Applications - Volume 153, Issues 5â6, 1 December 2005, Pages 724-734
نویسندگان
Edward Beckenstein, Lawrence Narici,