The purpose of this paper is to introduce and discuss the concept of orthogonality in normed spaces. A concept of orthogonality on normed linear space was introduced. We obtain some subspaces of Banach spaces which are topologically complemented.

The Banach space `∞/c0 is isomorphic to the linear space of continuous functions on N∗ with the supremum norm, C(N∗). Similarly, the canonical representation of the `∞ sum of `∞/c0 is the Banach space of continuous functions on the closure of any non-compact cozero subset of N∗. It is important to determine if there is a continuous linear lifting of this Banach space to a complemented subset of...

We are interested here in isomorphic invariants of the various Banach spaces associated with the spaces L°°Gu) for finite measures ju. (Throughout, "/*" and v denote arbitrary finite measures on possibly different unspecified measureable spaces.) We classify the spaces L°°(M) themselves up to isomorphism (linear homeomorphism) in §3, where we also obtain information on the spaces A and A* for s...

If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A0, A1) such that A0 and A1 are isometric to X ⊕ V , and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic to Z. Thus many properties of Banach spaces, including having non-trivial cotype, hav...

In 1965, Ron Douglas proved that if X is a closed subspace of an L-space and X is isometric to another L-space, then X is the range of a contractive projection on the containing L-space. In 1977 Arazy-Friedman showed that if a subspace X of C1 is isometric to another C1-space (possibly finite dimensional), then there is a contractive projection of C1 onto X. In 1993 Kirchberg proved that if a s...

It is shown that the invariant subspace of the Bergman space Ap of the unit disc, generated by a finite union of Hardy interpolation sequences, is complemented in Ap. Let D be the open unit disc of the complex plane C, and let H = H(D) denote the usual Hardy space. For 0 < p < ∞ the Bergman space A consists of analytic functions f on D such that ‖f‖p = ∫ D |f(z)| dA(z) < ∞, where dA is area mea...

An operator is unicellular if its lattice of invariant subspaces is totally ordered by inclusion. The list of nests which are known to be the set of invariant subspaces of a unicellular operator is surprisingly short. We construct unicellular operators on lp, 1 ^ p < oo, and on c0 with lattices isomorphic to a + X + ß* where a and ß are countable (finite or zero) ordinals, and X is in this shor...