Norm property of Hilbert pairing

The concept of canonical dual K-Bessel sequences was recently introduced, a deep study of which is helpful in further developing and enriching the duality theory of K-frames. In this paper we pay attention to investigating the structure of the canonical dual K-Bessel sequence of a Parseval K-frame and some derived properties. We present the exact form of the canonical dual K-Bessel sequence of a Parseval K-frame, and a necessary and sufficient condition for a dual K-Bessel sequence of a given Parseval K-frame to be the canonical dual K-Bessel sequence is investigated. We also give a necessary and sufficient condition for a Parseval K-frame to have a unique dual K-Bessel sequence and equivalently characterize the condition under which the canonical dual K-Bessel sequence of a Parseval K-frame admits a unique dual K⁎-Bessel sequence. Finally, we obtain a minimal norm property on expansion coefficients of elements in the range of K resulting from the canonical dual K-Bessel sequence of a Parseval K-frame.

Positivity of vector bundles and Hodge theory

International Journal of Mathematics ◽

10.1142/s0129167x21400085 ◽

2021 ◽

pp. 2140008

Author(s):

Mark Green ◽

Phillip Griffiths

Keyword(s):

Differential Geometry ◽

Vector Bundles ◽

Special Property ◽

Hodge Theory ◽

Algebraic Varieties ◽

Hodge Structures ◽

Curvature Invariants ◽

Norm Property ◽

Expository Paper

Differential geometry, especially the use of curvature, plays a central role in modern Hodge theory. The vector bundles that occur in the theory (Hodge bundles) have metrics given by the polarizations of the Hodge structures, and the sign and singularity properties of the resulting curvatures have far reaching implications in the geometry of families of algebraic varieties. A special property of the curvatures is that they are [Formula: see text] order invariants expressed in terms of the norms of algebro-geometric bundle mappings. This partly expository paper will explain some of the positivity and singularity properties of the curvature invariants that arise in the Hodge theory with special emphasis on the norm property.

On a norm property of Hilbert symbol over polynomial formal module in multidimensional local field

Vestnik of Saint Petersburg University Mathematics Mechanics Astronomy ◽

10.21638/11701/spbu01.2016.404 ◽

2016 ◽

Vol 3(61) (4) ◽

pp. 552-557

Author(s):

Vladislav V. Volkov ◽

Keyword(s):

Local Field ◽

Hilbert Symbol ◽

Formal Module ◽

Norm Property

Appendix 3: Minimum norm property of projections

Adaptive Array Principles ◽

10.1049/pbew011e_appendix3 ◽

2011 ◽

pp. 247-247

Keyword(s):

Minimum Norm ◽

Norm Property

On the norm property of G(c)-radii and Eaton triples

Linear Algebra and its Applications ◽

10.1016/s0024-3795(01)00310-x ◽

2001 ◽

Vol 336 (1-3) ◽

pp. 119-130 ◽

Cited By ~ 6

Author(s):

M. Niezgoda ◽

Tin-Yau Tam

Keyword(s):

Norm Property

Rings with Finite Norm Property

Canadian Journal of Mathematics ◽

10.4153/cjm-1972-049-1 ◽

1972 ◽

Vol 24 (4) ◽

pp. 557-565 ◽

Cited By ~ 10

Author(s):

Kathleen B. Levitz ◽

Joe L. Mott

Keyword(s):

Abelian Group ◽

Structural Properties ◽

Homomorphic Image ◽

Finite Rings ◽

Residually Finite ◽

Finite Norm ◽

Norm Property

A ring A has finite norm properly, abbreviated FNP, if each proper homomorphic image of A is finite. In [3], Chew and Lawn described some of the structural properties of FNP rings with identity, which they called residually finite rings. The twofold aim of this paper is to extend the results of [3] to arbitrary rings with FNP and to give characterizations of FNP rings independent of the results of [3].If A is a ring, let A+ denote A regarded as an abelian group. In the first section of this paper, we explore the effects of FNP upon the structure of A+. The following theorem is typical of the results in this section.