On Banach spaces with unconditional bases

LetX be a Banach space with a sequence of linear, bounded finite rank operatorsR _n:X→X such thatR _nR_m=R_min(_n,m) ifn≠m and lim _n→∞ R _n x=x for allx∈X. We prove that, ifR _n−R_n −1 factors uniformly through somel _p and satisfies a certain additional symmetry condition, thenX has an unconditional basis. As an application, we study conditions on Λ ⊂ ℤ such thatL _Λ=closed span , where , has an unconditional basis. Examples include the Hardy space .     

EveryL 1-predual is complemented in a simplex space

We show that everyL ₁-predual space is complemented in a simplex space. This answers a question raised by Lazar and Lindenstrauss.     

On weighted spaces of holomorphic functions of several variables

We generalize the results of [11] and [12] for the unit ball $ \mathbb{B}_d $ \mathbb{B}_d of ℂ ^d . In particular, we show that under the weight condition (B) the weighted H ^∞-space on $ \mathbb{B}_d $ \mathbb{B}_d is isomorphic to ℓ^∞ and thus complemented in the corresponding weighted L ^∞-space. We construct concrete, generalized Bergman projections accordingly. We also consider the case where the domain is the entire space ℂ ^d . In addition, we show that for the polydisc $ \mathbb{D}^d $ \mathbb{D}^d ^d , the weighted H ^∞-space is never isomorphic to ℓ^∞.     

On primary simplex spaces

We give an example of a primary separable simplex space with non-separable dual which is not isomorphic to C() or to the Poulsen simplex space A(S_p).During the preparation of this paper the author was partly supported by the Deutsche Forschungsgemeinschaft     

Duals of holomorphic Besov spaces on the polydisks and diagonal mappings

Let U ⁿ be the unit polydisk in C ⁿ and S be the space of functions of regular variation. Let 1 ≤ p < ∞, ω = (ω ₁, ..., ω _n ), ω _j ∈ S(1 ≤ j ≤ n) and f ∈ H(U ⁿ ). The function f is said to be in holomorphic Besov space B _p (ω) if

Simultaneous determination of aflatoxins, ochratoxin A, and zearalenone in grains by new immunoaffinity column/liquid chromatography

The simultaneous determination of mycotoxins was performed in 3 steps: extraction, cleanup, and detection. For extraction, a mixture of acetonitrile-water (60 + 40, v/v) was proved appropriate. For cleanup, a new Afla-Ochra-Zea immunoaffinity column was used. After derivatization with trifluoroacetic acid, the mycotoxins aflatoxins, ochratoxin A (OTA), and zearalenone (ZEA) were determined simultaneously by liquid chromatography with fluorescence detection. The detection limits in different matrixes after cleanup with the new immunoaffinity column were very low: aflatoxins, 0.002-0.7 microg/kg; OTA, 0.07-0.25 microg/kg; ZEA, 1-3 microg/kg. The limits of determination were: aflatoxins, 0.25 microg/kg; OTA, 0.5 microg/kg; ZEA, 5 microg/kg. The recovery rates for aflatoxins, OTA, and ZEA for rye and rice were between 86 and 93% when a 0.5 g sample matter per immunoaffinity column was used.     

On Weighted Spaces of Harmonic and Holomorphic Functions

Weighed spaces of harmonic and holomorphic functions on theunit disc are studied. We show that for all radial weights whichare not decreasing too fast the space of harmonic functionsis isomorphic to c₀. For the weights that we consider we completelycharacterize those spaces of holomorphic functions which areisomorphic to c₀. Moreover, we determine when the Riesz projection,mapping the weighted space of harmonic functions onto the correspondingspace of holomorphic functions, is bounded.     

On the Structure of Hv0(D) and hv0(D)

Weighted spaces of harmonic and holomorphic functions on the unit disc are discussed. It is shown that these spaces are always subspaces of c₀. Moreover, for many weights, it is shown that the weighted space of holomorphic functions has a basis.