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Bulletin of the Australian Mathematical Society, 2019
We show that if $(X,\Vert \cdot \Vert )$ is a Banach space that admits an equivalent locally uniformly rotund norm and the set of all norm-attaining functionals is residual then the dual norm $\Vert \cdot \Vert ^{\ast }$ on $X^{\ast }$ is Fréchet at
Moors, Warren B., Tan, Neşet Özkan
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We show that if $(X,\Vert \cdot \Vert )$ is a Banach space that admits an equivalent locally uniformly rotund norm and the set of all norm-attaining functionals is residual then the dual norm $\Vert \cdot \Vert ^{\ast }$ on $X^{\ast }$ is Fréchet at
Moors, Warren B., Tan, Neşet Özkan
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1995
Linear functionals and the dual space of a vector space are defined and characterized. Every vector space is shown to be canonically embeddable in its second dual. Maximal subspaces are characterized as kernels of nontrivial linear functionals. The trace of a square matrix is studied in detail. Over a field of characteristic 0, a square matrix is shown
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Linear functionals and the dual space of a vector space are defined and characterized. Every vector space is shown to be canonically embeddable in its second dual. Maximal subspaces are characterized as kernels of nontrivial linear functionals. The trace of a square matrix is studied in detail. Over a field of characteristic 0, a square matrix is shown
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CHI '11 Extended Abstracts on Human Factors in Computing Systems, 2011
Dual-Space Drawing is an interface that enables children to express their drawing ideas in both the digital and real worlds. It supports creative and reflective drawing experiences using two layers: a transparent layer and a screen layer. The interface takes a user's drawing movements on the transparent display unobtrusively and then projects the ...
Jee Yeon Hwang +2 more
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Dual-Space Drawing is an interface that enables children to express their drawing ideas in both the digital and real worlds. It supports creative and reflective drawing experiences using two layers: a transparent layer and a screen layer. The interface takes a user's drawing movements on the transparent display unobtrusively and then projects the ...
Jee Yeon Hwang +2 more
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Dual quaternions and dual projective spaces
Chaos, Solitons & Fractals, 2009Abstract In this study, dual unitary matrices SUD(2) were obtained. We correspond to one to one elements of the unit dual sphere S D 3 with the dual unitary matrices SUD(2). Thus, we express spherical concepts such as meridians of longitude and parallels of latitude on SUD(2).
Ata, Erhan, Yaylı, Yusuf
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1984
This chapter is intended as a prerequisite for later chapters. In it we introduce a topology on the dual of a topological vector space. We present some of the standard results in the theory of Frechet spaces and some additional results on topological vector spaces in general.
D. H. Luecking, L. A. Rubel
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This chapter is intended as a prerequisite for later chapters. In it we introduce a topology on the dual of a topological vector space. We present some of the standard results in the theory of Frechet spaces and some additional results on topological vector spaces in general.
D. H. Luecking, L. A. Rubel
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