The phrase "an unconditional basis" is correct and usable in written English.
It can be used to describe a situation or agreement that is not subject to any conditions or limitations.
Example: "The support was provided on an unconditional basis, ensuring that all participants felt secure and valued."
Alternatives: "a non-negotiable foundation" or "a fundamental basis without conditions".
Then we give a criterion for sequences of reproducing kernels which form an unconditional basis in their closed linear span.
The main step in our proof is to show that a vector Haar system forms an unconditional basis inL2(W).
We show that for each Banach space X which has a dual with an unconditional basis (x*i), the approximable (nuclear) m-homogeneous polynomials on X have an unconditional basis if and only if the monomial basis with respect to (x*i) is unconditional.
Bishop Daily had said this month that the diocese would begin reporting accusations to law enforcement authorities on an unconditional basis, revising a policy under which charges were first evaluated internally.
"They will initially purchase on an unconditional basis €241m of the state's shareholding and are further committing to purchase the remainder of up to €882m after appropriate regulatory approvals have been obtained," the government statement said.
No infinite dimensional Banach space X is known which has the property that for m⩾2 the Banach space of all continuous m-homogeneous polynomials on X has an unconditional basis.
It is evident that if the space has a unconditional basis, if is small enough, the above result remains true for some.
We also give a formula for the Szlenk power type of the E-direct sum of separable spaces provided that E has a shrinking unconditional basis whose dual basis yields an asymptotic ℓp structure in E⁎.
His publications included New Classes of Lp-Spaces (1981) and, with A. Casazza, J. Lindenstrauss, and L. Tzafriri, Banach Spaces with a Unique Unconditional Basis, up to Permutation (1985).
In particular, we show that an UFO with unconditional basis must be either c0 or a superreflexive weak type 2 space; that a hereditarily UFO Köthe function space must be Hilbert; and that a rearrangement invariant space UFO must be either L∞ or a superreflexive type 2 Banach lattice.
It is a useful tool of digging asymptotic structure of Banach space, and it is a class of asymptotic unconditional basis.
