[amal]

I have an electrolyte solution ( kcl) in electrochemical cell the electrodes are made of silver. I want to calculate the minimum potential difference to start the electrolysis reaction.

My purpose is to prevent these reaction form happening, I want to my electrolytes solution to be conductive, so electrolysis is not favorable.

any word on this subject will be helpful

Thanks

[Pulverulescent]

I want to my electrolytes solution to be conductive, so electrolysis is not favorable.

An electrolyte is any medium which conducts electricity by ionic means.
Current-transfer by ionic means is electrolysis.

[Arkcon]

Its a little hard to understand your application, amal:, but it appears you need a conductive solution that won't decompose.  We use such solutions to manufacture electrolytic capacitors.  Maybe the solutions used in them will suit your application?
http://en.wikipedia.org/wiki/Electrolytic_capacitor#Electrolyte

[Borek]

Current-transfer by ionic means is electrolysis.

That's a lousy wording.

Current in the bulk of the solution doesn't require electrolysis. However, you need an electrode reaction to move the charge through the phase boundary.