Question about finite dimensional real l^p space

[larkin1993]

I believe I understand the definitition of the l^p space, its set of infinite sequences that converge when the sequence is put to the power of p, term by term. However I came across "Let T be a real linear operator from a finite dimensional real l^p space to a real finite dimensional banach space". My issue is that I don't understand what it means by a real finite dimensional real l^p space. If anyone could point me in the right direction that would be great.

 

[micromass]

They just mean $\mathbb{R}^n$ with norm

\|(x_1,...,x_n)\|_p = \sqrt[p]{\sum_{k=1}^n |x_k|^p}

 

[larkin1993]

Ahh that makes a lot more sense. Thank you