The F. and M. riesz theorem for vector measures

Ryan, Robert D.

doi:10.1016/s1385-7258(63)50041-9

Cited by 20 publications

(15 citation statements)

References 6 publications

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“…J -X Ryan [10] offers an account of the study of dual spaces of spaces of continuous functions from a compact Hausdorff space to a Banach space X. These results describe the dual as a space of vector-valued measures taking values in X*.…”

Section: J -Nmentioning

confidence: 99%

Bounded and compact vectorial Hankel operators

Page¹

1970

Trans. Amer. Math. Soc.

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Abstract. Operators H satisfying S*H=HSwhere S is a unilateral shift on Hubert space are called Hankel operators. For a fixed shift S of arbitrary multiplicity the Banach spaces of bounded Hankel operators and of compact Hankel operators are described, and it is shown that the former is always the second dual of the latter. Representations for bounded and for compact Hankel operators are given in a standard function space model.

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Section: J -Nmentioning

confidence: 99%

Bounded and compact vectorial Hankel operators

Page¹

1970

Trans. Amer. Math. Soc.

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“…We will return to these processes in the next section. We conclude this section by reporting on the findings of [45,46] (see also [47]). There, the authors employed the lattice formulation of NRQCD to access bb bound states on the lattice at finite temperature.…”

Section: Pos(confinement X)004mentioning

confidence: 87%

Review of EFT treatment of quarkonium at finite temperature

Ghiglieri¹

2013

Proceedings of XTH Quark Confinement and the Hadron Spectrum — PoS(Confinement X)

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Heavy quarkonium is one of the most investigated probes of the medium produced in heavy-ion collisions. In the past few years progress has been made in the description of its in-medium dynamics from QCD. Non-relativistic EFTs in particular allow one to define and compute rigorously the potential governing the real-time evolution of the bound state from QCD, showing that it is composed of a real and an imaginary part. The latter encodes the effect of scattering with the light constituents of the plasma and is oftentimes responsible for the dissociation of the bound state. The EFT approach and its main results, as well as comparisons with recent lattice data and phenomenological applications, are briefly reviewed here.

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“…The next statement is well known and, apparently, was reproved many times in different generality (see, e.g., the references in [6], which range from 1936 to 1959). From a modern viewpoint, this statement can be deduced from general duality theorems for operator spaces, without a repetition of the proof of the Riesz representation theorem for the space of scalar functions.…”

Section: The Space Xmentioning

confidence: 90%

“…They should be understood in the sense of the weak topology (note that we used the same framework in the preceding item). The situation was clarified as early as in [6] (see also [7]; note that the paper [8] contains a revision of the work presented in [6] and [7] from a somewhat more general viewpoint; references to other papers on the same subject and published roughly at the same time period can also be found in [8]). We describe the results in more detail.…”

Section: The Space Xmentioning

confidence: 99%

“…The Fourier coefficients of λ with negative indices vanish (the integrals defining the Fourier coefficients and, more generally, the integrals ϕ dλ, where ϕ is a scalar function, are understood in the Gelfand sense: we mean the element x → ϕ d x, λ , x ∈ G, of G * ). By the main result of [6], there exists a G-measurable G * -valued function f such that λ(e) = e f dm for all Borel sets e ⊂ T (again, the integral is understood in a weak sense). Next, the scalar-valued function t → f (t) G * may fail to be measurable.…”

Section: The Space Xmentioning

confidence: 99%

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Some remarks to the corona theorem

Kislyakov

Rutsky

2013

St. Petersburg Math. J.

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With the help of a fixed point theorem, in §1 it is shown that the so-called L ∞ -and L p -corona problems are equivalent in the general situation. This equivalence extends to the case where L p is replaced by a more or less arbitrary Banach lattice of measurable functions on the circle. In §2, the corona theorem for 2 -valued analytic functions is exploited to give a new proof for the existence of an analytic partition of unity subordinate to a weight with logarithm in BMO. In §3, simple observations are presented that make it possible to pass from one sequence space to another in L ∞ -estimates for solutions of corona problems.2010 Mathematics Subject Classification. Primary 30H80.

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The F. and M. riesz theorem for vector measures

Cited by 20 publications

References 6 publications

Bounded and compact vectorial Hankel operators

Bounded and compact vectorial Hankel operators

Review of EFT treatment of quarkonium at finite temperature

Some remarks to the corona theorem

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