N is said to be ............ to N' if there exists an isometric isomorphism of N onto N'.

A Banach space is a .................. space.

The ........... theorem enables us to give a satisfactory description of the projections on a Banach space.

$$\left|\left|x\right|\right|$$ is a real function defined on N, this function is called the ................ of N.

The norm of a number x is defined by .....................

The norm $$\left|\left|f\right|\right|=\ \sup\ \left|f\left(x\right)\right|$$ is sometimes called the ............

Let N be a non-zero normed linear space then N is a Banach space iff $$\left\{x:\left|\left|x\right|\right|=1\right\}$$ is ......................

The elements of N* are called ............................

Which of the following is an example of a nls?

The weak topology on a nls N is a weakest topology on N with respect in which all the functions in N* are ...................

The weak* topology is the weak topology on N* generated y all the ..................Fx in N**

Say true or false: S* is compact in the weak topology iff N is finite dimensional.

S* is compact in the strong topology iff N is reflexive.

If B and B' are Banach spaces, and if T is a continuous linear transformation of B onto B'. Then T is an ...................... mapping.

A projection E on a linear space L is an idempotent linear transformation of L into ......................

Say true or false: If B and B' are Banach spaces and if T is a L.T of B into B', then T is closed iff its graph is closed.

A non -empty subset X of a nls N is ounded iff f(X) is a................... set of numbers for each f in N*.

$$S_{10}$$ = ..............

S(13, 5) = ...............

Which among these is Prof. Von Neumann