You need two additional assumptions: the operator $A$ has to be a so-called cosine function generator, and your product space has to be $V\times H$ with a space $V\subset H$. 

Cosine function generator is more than sectorial, it is moreor less when the numerical range of $A$ is in a parabola (selfadjoint negative semidefinite is ok).

The space $V$ is difficult, but if $A$ is selfadjoint, then it is essentially $D(A^{1/2})$.

See Section VI.3 in

> <cite cite="ISBN: 0-387-98463-1" mrnumber="1721989"
> authors="Klaus-Jochen Engel and Rainer Nagel">_Klaus-Jochen Engel and
> Rainer Nagel_, MR 1721989 [**One-parameter semigroups for linear
> evolution
> equations**](http://www.ams.org/mathscinet-getitem?mr=1721989), ISBN:
> 0-387-98463-1.</cite>

or Section 7.4 in

> Haase, Markus [The functional calculus for sectorial operators][1].
> Operator Theory: Advances and Applications, 169. Birkhäuser Verlag,
> Basel, 2006. xiv+392 pp. ISBN: 978-3-7643-7697-0; 3-7643-7697-X

  [1]: http://www.springer.com/de/book/9783764376970