Polynomial Grothendieck properties

Details Polynomial Grothendieck properties Polynomial Grothendieck properties

1994-04-25

arxiv.org/abs/math/9404214v1

Glasgow Math. J. 37 (1995), 211-219

Mathematics

Functional Analysis

Scientific paper

A Banach space $E$ has the Grothendieck property if every (linear bounded) operator from $E$ into $c_0$ is weakly compact. It is proved that, for an integer $k>1$, every $k$-homogeneous polynomial from $E$ into $c_0$ is weakly compact if and only if the space ${\cal P}(^kE)$ of scalar valued polynomials on $E$ is reflexive. This is equivalent to the symmetric $k$-fold projective tensor product of $E$ (i.e., the predual of ${\cal P}(^kE)$) having the Grothendieck property. The Grothendieck property of the projective tensor product $E\widehat{\bigotimes}F$ is also characterized. Moreover, the Grothendieck property of $E$ is described in terms of sequences of polynomials. Finally, it is shown that if every operator from $E$ into $c_0$ is completely continuous, then so is every polynomial between these spaces.

Affiliated with

Also associated with

No associations

Rating

Polynomial Grothendieck properties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Polynomial Grothendieck properties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Polynomial Grothendieck properties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-262511