template <class T>
class mydeque : private std::deque<T>
{
    using std::deque<T>::operator[];
};

А>template <class T>
А>class mydeque : private std::deque<T>
А>{
А>    using std::deque<T>::operator[];
А>};
А>

А>а конкретно компилер ругается на отсутствие включаемого члена (оператора индекса).

template <class T>
class mydeque : private std::deque<T>
{
   typedef std::deque<T> Base;
   using Base::operator[];
};

B>>template <class T>
B>>class mydeque : private std::deque<T>
B>>{
B>>   typedef std::deque<T> Base;
B>>   using Base::operator[];
B>>};
B>>

B>>Если нет — то остается только брать в руки бубен...

А>те же яйца — member identifier expected ((((((((((

std::deque<T>::reference operator[](std::size_t index)    { return deque<T>::operator[](index); }

А>template <class T>
А>class mydeque : private std::deque<T>
А>{
А>    using std::deque<T>::operator[];
А>};
А>

А>а конкретно компилер ругается на отсутствие включаемого члена (оператора индекса).

std::deque<T>::operator[];

А>>template <class T>
А>>class mydeque : private std::deque<T>
А>>{
А>>    using std::deque<T>::operator[];
А>>};
А>>

А>>а конкретно компилер ругается на отсутствие включаемого члена (оператора индекса).

RO>std::deque<T>::operator[];
RO>

7.3.3/16
[Note: use of access-declarations (11.3) is deprecated; member using-declarations provide a better alternative.]

11.3/1
The access of a member of a base class can be changed in the derived class by mentioning its qualified-id in the derived class declaration. Such mention is called an access declaration. The effect of an access declaration qualified-id ; is defined to be equivalent to the declaration using qualified-id ; 100)
100) Access declarations are deprecated; member using-declarations (7.3.3) provide a better means of doing the same things. In earlier
versions of the C + + language, access declarations were more limited; they were generalized and made equivalent to using-declarations.

7.3.3/3
Every using-declaration is a declaration and a member-declaration and so can be used in a class definition.

7.3.3/4
A using-declaration used as a member-declaration shall refer to a member of a base class of the class being defined, shall refer to a member of an anonymous union that is a member of a base class of the class being defined, or shall refer to an enumerator for an enumeration type that is a member of a base class of the class being defined.