scholarly journals ON THE REPRESENTATION OF MULTI-IDEALS BY TENSOR NORMS

2011 ◽  
Vol 90 (2) ◽  
pp. 253-269 ◽  
Author(s):  
GERALDO BOTELHO ◽  
ERHAN ÇALIŞKAN ◽  
DANIEL PELLEGRINO
Keyword(s):  
Isometric Isomorphism ◽  
Multilinear Forms ◽  
Tensor Norm ◽  
Tensor Norms ◽  
Image Position

AbstractA tensor norm β=(βn)∞n=1 is smooth if the natural correspondence where 𝕂=ℝ or ℂ, is always an isometric isomorphism. In this paper we study the representation of multi-ideals and of ideals of multilinear forms by smooth tensor norms.

Tensor Products of Operator Spaces II

1991 ◽  
Vol 44 (1) ◽  
pp. 75-90 ◽  
Author(s):  
David P. Blecher
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Elementary Theory ◽  
Tensor Products ◽  
Space Theory ◽  
Operator Spaces ◽  
Tensor Norm ◽  
Tensor Norms

AbstractTogether with Vern Paulsen we were able to show that the elementary theory of tensor norms of Banach spaces carries over to operator spaces. We suggested that the Grothendieck tensor norm program, which was of course enormously important in the development of Banach space theory, be carried out for operator spaces. Some of this has been done by the authors mentioned above, and by Effros and Ruan. We give alternative developments of some of this work, and otherwise continue the tensor norm program.

On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces

2010 ◽  
Vol 53 (4) ◽  
pp. 690-705
Author(s):  
M. E. Puerta ◽  
G. Loaiza
Keyword(s):  
Maximal Operator ◽  
Interpolation Space ◽  
Sufficient Conditions ◽  
Classical Approach ◽  
Operator Ideals ◽  
Metric Properties ◽  
Real Method ◽  
Tensor Norm ◽  
Tensor Norms ◽  
Necessary And Sufficient

AbstractThe classical approach to studying operator ideals using tensor norms mainly focuses on those tensor norms and operator ideals defined by means of ℓp spaces. In a previous paper, an interpolation space, defined via the real method and using ℓp spaces, was used to define a tensor norm, and the associated minimal operator ideals were characterized. In this paper, the next natural step is taken, that is, the corresponding maximal operator ideals are characterized. As an application, necessary and sufficient conditions for the coincidence of the maximal and minimal ideals are given. Finally, the previous results are used in order to find some new metric properties of the mentioned tensor norm.

scholarly journals Approximation properties of tensor norms and operator ideals for Banach spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 1698-1708
Author(s):  
Ju Myung Kim
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Approximation Property ◽  
Approximation Properties ◽  
Operator Ideals ◽  
Finitely Generated ◽  
Tensor Norm ◽  
Tensor Norms

Abstract For a finitely generated tensor norm α \alpha , we investigate the α \alpha -approximation property ( α \alpha -AP) and the bounded α \alpha -approximation property (bounded α \alpha -AP) in terms of some approximation properties of operator ideals. We prove that a Banach space X has the λ \lambda -bounded α p , q {\alpha }_{p,q} -AP ( 1 ≤ p , q ≤ ∞ , 1 / p + 1 / q ≥ 1 ) (1\le p,q\le \infty ,1/p+1/q\ge 1) if it has the λ \lambda -bounded g p {g}_{p} -AP. As a consequence, it follows that if a Banach space X has the λ \lambda -bounded g p {g}_{p} -AP, then X has the λ \lambda -bounded w p {w}_{p} -AP.

A non-commutative Gel'fand-Naimark theorem

1980 ◽  
Vol 88 (3) ◽  
pp. 425-428 ◽  
Author(s):  
Christopher J. Mulvey
Keyword(s):  
Maximal Ideal ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Isometric Isomorphism ◽  
C Algebra ◽  
C Algebras ◽  
Image Position ◽  
Straightforward Proof

This paper presents a straightforward proof of the Gel'fand-Naimark theorem for non-commutative C*-algebras with identity, established by Dauns and Hofmann(2) in the context of fields of C*-algebras, by considering instead C*-algebras in categories of sheaves. The proof differs from that of (2,3,4) in obtaining an isometric *-isomorphismfrom the C*-algebra A to the C*-algebra of sections of a C*-algebra Ax in the category of sheaves on the maximal ideal space X of the centre of A, without invoking any arguments which involve completeness (3, Theorem 7·9). Instead, the results of (7) yield immediately the existence of an algebraic isomorphism, the compactness of the maximal ideal space X then being used to prove that Ax is indeed a C*-algebra in the category of sheaves on X and that the isomorphism is isometric. One recovers the representation of (2) by noting (8) that any C*-algebra in the category of sheaves on X is isomorphic to the sheaf of sections of a canonical field of C*-algebras on X.

scholarly journals Operator ideals and tensor norms defined by a sequence space

2004 ◽  
Vol 69 (3) ◽  
pp. 499-517 ◽  
Author(s):  
J.A. López Molina ◽  
M.J. Rivera
Keyword(s):  
Classical Theory ◽  
Sequence Space ◽  
Maximal Operator ◽  
Dimensional Structure ◽  
Operator Ideals ◽  
Finite Dimensional ◽  
Tensor Norm ◽  
Tensor Norms

We study the tensor norm defined by a sequence space λ and its minimal and maximal operator ideals associated in the sense of Defant and Floret. Our results extend the classical theory related to the tensor norms of Saphar [16]. They show the key role played by the finite dimensional structure of the ultrapowers of λ in this kind of problems.

scholarly journals (n + 1)-TENSOR NORMS OF LAPRESTÉ'S TYPE

2012 ◽  
Vol 54 (3) ◽  
pp. 665-692 ◽  
Author(s):  
J. A. LÓPEZ MOLINA
Keyword(s):  
Linear Operator ◽  
Tensor Product ◽  
Tensor Products ◽  
Operator Ideals ◽  
Tensor Norm ◽  
Tensor Norms

AbstractWe study an (n + 1)-tensor norm αr extending to (n + 1)-fold tensor products, the classical one of Lapresté in the case n = 1. We characterise the maps of the minimal and the maximal multi-linear operator ideals related to αr in the sense of Defant and Floret (A. Defant and K. Floret, Tensor norms and operator ideals, North Holland Mathematical Studies, no. 176 (North Holland, Amsterdam, Netherlands, 1993). As an application we give a complete description of the reflexivity of the αr-tensor product (⊗j = 1n + 1 ℓuj, αr).

Simple Identification of Electron Diffraction Ring Patterns

1969 ◽  
Vol 27 ◽  
pp. 160-161
Author(s):  
Carolyn Nohr ◽  
Ann Ayres
Keyword(s):  
Electron Microscope ◽  
Electron Diffraction ◽  
Diffraction Ring ◽  
Image Position

Texts on electron diffraction recommend that the camera constant of the electron microscope be determine d by calibration with a standard crystalline specimen, using the equation

Atomic orientation effects in proton stopping at low velocity

1983 ◽  
Vol 41 ◽  
pp. 708-709
Author(s):  
Kin Lam
Keyword(s):  
Polycrystalline Material ◽  
Charged Particles ◽  
Target Material ◽  
Stopping Power ◽  
Low Velocity ◽  
Electronic Density ◽  
Interatomic Distances ◽  
Frame Work ◽  
Image Position ◽  
Atomic Orientation

The energy of moving ions in solid is dependent on the electronic density as well as the atomic structural properties of the target material. These factors contribute to the observable effects in polycrystalline material using the scanning ion microscope. Here we outline a method to investigate the dependence of low velocity proton stopping on interatomic distances and orientations.The interaction of charged particles with atoms in the frame work of the Fermi gas model was proposed by Lindhard. For a system of atoms, the electronic Lindhard stopping power can be generalized to the formwhere the stopping power function is defined as

A Magnetic Spectrometer for a Scanning Transmission Electron Microscope

1974 ◽  
Vol 32 ◽  
pp. 436-437
Author(s):  
A. Kosiara ◽  
J. W. Wiggins ◽  
M. Beer
Keyword(s):  
Scanning Transmission Electron Microscope ◽  
Magnetic Spectrometer ◽  
Fringe Field ◽  
Curvature Radius ◽  
Magnetic Pole ◽  
Quadrupole Field ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Under Construction ◽  
Image Position

A magnetic spectrometer to be attached to the Johns Hopkins S. T. E. M. is under construction. Its main purpose will be to investigate electron interactions with biological molecules in the energy range of 40 KeV to 100 KeV. The spectrometer is of the type described by Kerwin and by Crewe Its magnetic pole boundary is given by the equationwhere R is the electron curvature radius. In our case, R = 15 cm. The electron beam will be deflected by an angle of 90°. The distance between the electron source and the pole boundary will be 30 cm. A linear fringe field will be generated by a quadrupole field arrangement. This is accomplished by a grounded mirror plate and a 45° taper of the magnetic pole.

Optimizing conditions for x-ray microchemical analysis in analytical electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 548-549 ◽  
Author(s):  
N. J. Zaluzec
Keyword(s):  
Solid Angle ◽  
Analytical Electron Microscopy ◽  
Incident Beam ◽  
Thin Foil ◽  
Experimental Conditions ◽  
X Ray ◽  
Microchemical Analysis ◽  
Analytical Electron ◽  
Image Position ◽  
Incident Beam Energy

The ultimate sensitivity of microchemical analysis using x-ray emission rests in selecting those experimental conditions which will maximize the measured peak-to-background (P/B) ratio. This paper presents the results of calculations aimed at determining the influence of incident beam energy, detector/specimen geometry and specimen composition on the P/B ratio for ideally thin samples (i.e., the effects of scattering and absorption are considered negligible). As such it is assumed that the complications resulting from system peaks, bremsstrahlung fluorescence, electron tails and specimen contamination have been eliminated and that one needs only to consider the physics of the generation/emission process.The number of characteristic x-ray photons (Ip) emitted from a thin foil of thickness dt into the solid angle dΩ is given by the well-known equation

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