The 30-share BSE Sensex was trading higher by 84.17 points at 40,934.46 in n opening deals.
The 30-share BSE Sensex was down 119.42 points or 0.29 per cent to 40,556.03 in early deals.
The fresh trade war tensions along with unabated foreign fund outflows weighed heavily on the market sentiments, traders said.
PMI data for manufacturing and services sectors are scheduled to come this week which may also impact trading at the bourses.
Similarly, the broader NSE Nifty was quoting 38.45 points, or 0.32 per cent, down at 12,112.70.
After touching its lifetime high of 41,163.79 during the day, the 30-share Sensex rose by 109.56 points or 0.27 per cent.
After hitting its life-time high, Sensex pared some gains to trade 52.93 points higher at 41,073.54 in morning session.
Sensex rose by 199.31 points or 0.49 per cent to end at a new life-time high of 41,020.61 as 24 of its constituents ended in green.
The 30-share Sensex was trading 207.41 points, or 0.51 per cent, higher at 41,028.71 in morning session.
After scaling its record intra-day high of 41,120.28, the 30-share BSE Sensex settled 67.93 points, or 0.17 per cent, lower at 40,821.30.