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- W4238734900 abstract "Publisher SummaryThis chapter discusses the concept of Normed spaces. If (F,|•|) is a locally compact non-archimedean non-trivially valued division ring, then the closure of G′ ⊗ E in ℒb(G;E) is k(G;E). The existence of linear projections onto spherically complete subspaces is due to Monna. For the case of normed spaces over a complete non-trivially valued field (F,|•|) Beckenstein and Narici studied the Fredholm Alternative Theorem via their analogue of Riesz's Lemma. By considering M=E and T the identity operator on E, one sees that any normed space (E, ∥•∥E) with the norm-preserving extension property has the norm-one projection property. In the proof of (c)⇒(a) it was shown that for any non-archimedean normed space (E, ∥•∥), (I2)⇒(In), for every n ⩽ 3." @default.
- W4238734900 created "2022-05-12" @default.
- W4238734900 date "1982-01-01" @default.
- W4238734900 modified "2023-09-23" @default.
- W4238734900 title "Chapter 6 Normed Spaces" @default.
- W4238734900 doi "https://doi.org/10.1016/s0304-0208(08)70632-7" @default.
- W4238734900 hasPublicationYear "1982" @default.
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