Every Hilbert space frame has a Naimark complement

Reproducing Kernel Hilbert Space vs. Frame Estimates

We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn H into a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω. We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. We further give an explicit formula for th...

Every Body Has a Brain

[1] http://ebhb.morphonix.com/ [2] http://fireflyfoundation.wordpress.com/brain-games/every-body-has-a-brain/ [3] http://dev.cdgr.ucsb.edu/organizations/morphonix [4] http://dev.cdgr.ucsb.edu/category/genre/educational [5] http://dev.cdgr.ucsb.edu/category/genre/music/dance [6] http://dev.cdgr.ucsb.edu/category/topics/anatomy [7] http://dev.cdgr.ucsb.edu/category/topics/brain [8] http://dev.cdg...

Some Results on g-Frame Operator in Hilbert Space

The g-frame operator for g-frame in Hilbert space is introduced. The results of g-frame operator are presented. A sequence of operators Λ̄j∈J(where Λ̄ = ΛSg −1 ) is a g-frame for the Hilbert space H with frame bounds 1 B and 1 A . Frame identities for g-normalized tight frames are established. Results on direct sum of gframe operators on direct sum of Hilbert spaces are presented. Mathematics Sub...

Every Algorithm Has a POV

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...