Let $\hat{\bf H}$ be a $p\hat{N}\times p \hat{N}$ sparse matrix consisting of $p\times p$ blocks, where each block is of size $\hat{N}\times\hat{N}$. The values in $\hat{\bf H}$ is illustrated below (empty places are zero):
The infinite norm of $\hat{\bf H}$ is obviously 1, and I know infinite norm is no larger than any $p$-norm. My question is, is there an even smaller natural norm for this $\hat{\bf H}$?
The proof that infinite norm is no larger than any $p$-norm.
