The journal entry for tenant improvement allowance depends on who owns the improvements. If the lessee owns the improvements, then the lessor records it as a deferred credit amortized over the life the improvements or the lease term. Otherwise, it is a fixed asset, which depreciates over its useful life.
It is possible that the lessor and lessee entered a flow-through arrangement. This arrangement means that the lessee is reimbursed by the lessor for any improvements. If this is the case, there is no fixed asset to record. These reimbursements are simply offset by any future rent payments, so the lessor records the improvement as if it was rent.